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All questions of System of Forces for Mechanical Engineering Exam
There are two types of loading. The uniformly distributed and the non-uniformly distributed that is the one having two different values at corners.- a)The first part of the statement is false and other part is true
- b)The first part of the statement is false and other part is false too
- c)The first part of the statement is true and other part is false
- d)The first part of the statement is true and other part is true too
Correct answer is option 'D'. Can you explain this answer?
There are two types of loading. The uniformly distributed and the non-uniformly distributed that is the one having two different values at corners.
a)
The first part of the statement is false and other part is true
b)
The first part of the statement is false and other part is false too
c)
The first part of the statement is true and other part is false
d)
The first part of the statement is true and other part is true too
|
Kritika Shah answered |
The two forms of the loading are the uniformly distributed and the non-uniformly distributed that is the one having two different values at corners. The uniform distributed load is not having two different values of the load per unit meter on the corner.
The calculation of the moment about the axis and the moment about any point by a force applied on the body are different from each other.- a)True
- b)False
Correct answer is option 'A'. Can you explain this answer?
The calculation of the moment about the axis and the moment about any point by a force applied on the body are different from each other.
a)
True
b)
False
|
Sparsh Unni answered |
Understanding Moments in Mechanics
When analyzing forces acting on a body, it's essential to differentiate between the moment about an axis and the moment about a point. These concepts are fundamental in mechanical engineering.
Moment About an Axis
- The moment about an axis refers to the rotational effect of a force around a specified axis.
- It is calculated by taking the perpendicular distance from the axis to the line of action of the force and multiplying it by the force.
- This concept is crucial when analyzing systems that require rotational equilibrium.
Moment About a Point
- The moment about a point, on the other hand, considers the rotational effect of a force around a specific point in space.
- This is calculated by determining the perpendicular distance from the point to the line of action of the force, which is then multiplied by the force.
- This moment is essential for understanding how forces affect the stability and motion of a body.
Key Differences
- Reference: The axis is a line around which rotation occurs, while a point is a specific location.
- Calculation: The distances used in calculations differ, affecting the resulting moments.
- Application: Different scenarios in engineering, such as beam loading and structural analysis, may require one type of moment over the other.
Conclusion
The calculation of moment about an axis and about a point is inherently different due to their definitions, reference points, and applications. Therefore, the statement is indeed true: the moment about the axis and the moment about any point by a force applied on the body are different from each other. Understanding this distinction is critical for effective analysis in mechanical engineering.
When analyzing forces acting on a body, it's essential to differentiate between the moment about an axis and the moment about a point. These concepts are fundamental in mechanical engineering.
Moment About an Axis
- The moment about an axis refers to the rotational effect of a force around a specified axis.
- It is calculated by taking the perpendicular distance from the axis to the line of action of the force and multiplying it by the force.
- This concept is crucial when analyzing systems that require rotational equilibrium.
Moment About a Point
- The moment about a point, on the other hand, considers the rotational effect of a force around a specific point in space.
- This is calculated by determining the perpendicular distance from the point to the line of action of the force, which is then multiplied by the force.
- This moment is essential for understanding how forces affect the stability and motion of a body.
Key Differences
- Reference: The axis is a line around which rotation occurs, while a point is a specific location.
- Calculation: The distances used in calculations differ, affecting the resulting moments.
- Application: Different scenarios in engineering, such as beam loading and structural analysis, may require one type of moment over the other.
Conclusion
The calculation of moment about an axis and about a point is inherently different due to their definitions, reference points, and applications. Therefore, the statement is indeed true: the moment about the axis and the moment about any point by a force applied on the body are different from each other. Understanding this distinction is critical for effective analysis in mechanical engineering.
The axis vector in the calculation of the moment along the axis of rotation is the axis which is collinear with the force vector.- a)True
- b)False
Correct answer is option 'B'. Can you explain this answer?
The axis vector in the calculation of the moment along the axis of rotation is the axis which is collinear with the force vector.
a)
True
b)
False
|
Pranavi Gupta answered |
The statement is false. The axis vector in the calculation of the moment along the axis of rotation is not necessarily collinear with the force vector. The moment is a vector quantity that describes the rotational effect of a force about a particular axis of rotation. It is given by the cross product of the position vector and the force vector.
The moment vector is perpendicular to the plane formed by the position vector and the force vector, and its direction is determined by the right-hand rule. The axis of rotation is defined as the line along which the moment vector lies. It is important to note that the axis of rotation is not necessarily collinear with the force vector.
Explanation:
- The moment vector is given by the equation:
- \(\text{Moment} = \text{Position Vector} \times \text{Force Vector}\)
- The position vector is a vector that points from the axis of rotation to the point where the force is applied. It defines the location of the force with respect to the axis of rotation.
- The force vector is a vector that represents the magnitude and direction of the force being applied.
- The cross product of the position vector and the force vector gives the moment vector, which describes the rotational effect of the force about the axis of rotation.
- Since the moment vector is perpendicular to the plane formed by the position vector and the force vector, the axis of rotation is also perpendicular to this plane.
- Therefore, the axis of rotation is not necessarily collinear with the force vector. It depends on the orientation of the position vector and the force vector relative to each other.
- In general, the axis of rotation can be any line that is perpendicular to the plane formed by the position vector and the force vector, and it passes through the point of rotation.
- So, the statement that the axis vector in the calculation of the moment along the axis of rotation is collinear with the force vector is false.
The moment vector is perpendicular to the plane formed by the position vector and the force vector, and its direction is determined by the right-hand rule. The axis of rotation is defined as the line along which the moment vector lies. It is important to note that the axis of rotation is not necessarily collinear with the force vector.
Explanation:
- The moment vector is given by the equation:
- \(\text{Moment} = \text{Position Vector} \times \text{Force Vector}\)
- The position vector is a vector that points from the axis of rotation to the point where the force is applied. It defines the location of the force with respect to the axis of rotation.
- The force vector is a vector that represents the magnitude and direction of the force being applied.
- The cross product of the position vector and the force vector gives the moment vector, which describes the rotational effect of the force about the axis of rotation.
- Since the moment vector is perpendicular to the plane formed by the position vector and the force vector, the axis of rotation is also perpendicular to this plane.
- Therefore, the axis of rotation is not necessarily collinear with the force vector. It depends on the orientation of the position vector and the force vector relative to each other.
- In general, the axis of rotation can be any line that is perpendicular to the plane formed by the position vector and the force vector, and it passes through the point of rotation.
- So, the statement that the axis vector in the calculation of the moment along the axis of rotation is collinear with the force vector is false.
What if the moment of the force calculated about the axis is negative?- a)It means that the force is applied in the opposite direction as imagined
- b)It means that the direction of the motion is in the opposite sense as imagined
- c)It means that the radius vector is in the opposite sense as imagined
- d)Such calculation means that the calculations are wrongly done
Correct answer is option 'B'. Can you explain this answer?
What if the moment of the force calculated about the axis is negative?
a)
It means that the force is applied in the opposite direction as imagined
b)
It means that the direction of the motion is in the opposite sense as imagined
c)
It means that the radius vector is in the opposite sense as imagined
d)
Such calculation means that the calculations are wrongly done
|
Dipika Kulkarni answered |
Explanation:
Opposite Sense of Motion:
- When the moment of the force calculated about the axis is negative, it indicates that the direction of the motion is in the opposite sense as imagined.
- This means that the force applied tends to cause a rotational motion in the opposite direction to what was initially assumed.
- In simple terms, the negative sign signifies that the rotation caused by the force is opposite to the anticipated direction.
Example:
- For instance, if a force is applied in a clockwise direction but the calculated moment is negative, it implies that the actual motion induced by the force is counterclockwise.
Importance of Understanding:
- It is crucial to interpret the sign of the calculated moment correctly in engineering applications to ensure the accurate prediction of motion and behavior of the system.
- Incorrect interpretation can lead to errors in analysis, design, and decision-making processes.
In conclusion, when the moment of the force about the axis is negative, it signifies that the direction of the motion induced by the force is opposite to the assumed sense. This understanding is essential for accurate engineering calculations and predictions.
Opposite Sense of Motion:
- When the moment of the force calculated about the axis is negative, it indicates that the direction of the motion is in the opposite sense as imagined.
- This means that the force applied tends to cause a rotational motion in the opposite direction to what was initially assumed.
- In simple terms, the negative sign signifies that the rotation caused by the force is opposite to the anticipated direction.
Example:
- For instance, if a force is applied in a clockwise direction but the calculated moment is negative, it implies that the actual motion induced by the force is counterclockwise.
Importance of Understanding:
- It is crucial to interpret the sign of the calculated moment correctly in engineering applications to ensure the accurate prediction of motion and behavior of the system.
- Incorrect interpretation can lead to errors in analysis, design, and decision-making processes.
In conclusion, when the moment of the force about the axis is negative, it signifies that the direction of the motion induced by the force is opposite to the assumed sense. This understanding is essential for accurate engineering calculations and predictions.
If the non-Uniform loading is of the type of parabola then?- a)The net load will not be formed as all the forces will be cancelled
- b)The net force will act the centre of the parabola
- c)The net force will act on the base of the loading horizontally
- d)The net force will act at the centroid of the parabola
Correct answer is option 'D'. Can you explain this answer?
If the non-Uniform loading is of the type of parabola then?
a)
The net load will not be formed as all the forces will be cancelled
b)
The net force will act the centre of the parabola
c)
The net force will act on the base of the loading horizontally
d)
The net force will act at the centroid of the parabola
|
Kirti Bose answered |
The net force will act at the centroid of the parabola. Whether it be a parabola or the cubic curve the centroid is the only point at which the net force act. Force can’t be acted horizontally if the loading is vertical. Hence whatever be the shape of the loading, the centroid is the point of action of net force.
The moment axis is in the direction perpendicular to the plane of the force and the distance.- a)True
- b)False
Correct answer is option 'A'. Can you explain this answer?
The moment axis is in the direction perpendicular to the plane of the force and the distance.
a)
True
b)
False
|
Anirban Khanna answered |
The moment axis is always perpendicular to the planes of the force and the distance of the axis and the point of action of the force on the body. This means that the moment is the cross product of the force and the distance between the axis and the point of action of the force.
For two vectors A and B, what is A.B (if they have angle α between them)?- a)|A||B| cosα
- b)|A||B|
- c)√(|A||B|) cosα
- d)|A||B| sinα
Correct answer is option 'A'. Can you explain this answer?
For two vectors A and B, what is A.B (if they have angle α between them)?
a)
|A||B| cosα
b)
|A||B|
c)
√(|A||B|) cosα
d)
|A||B| sinα
|
Divyansh Goyal answered |
If A and B are two vectors and θ is the angle between them, A.B represents the dot product of A and B. The dot product of two vectors is defined as:
A.B = |A| |B| cos(θ),
where |A| and |B| represent the magnitudes of vectors A and B, respectively.
A.B = |A| |B| cos(θ),
where |A| and |B| represent the magnitudes of vectors A and B, respectively.
Force vector R is having a______________- a)Length of R and a specific direction
- b)Length of R
- c)A specific direction
- d)Length of magnitude equal to square root of R and a specific direction
Correct answer is option 'A'. Can you explain this answer?
Force vector R is having a______________
a)
Length of R and a specific direction
b)
Length of R
c)
A specific direction
d)
Length of magnitude equal to square root of R and a specific direction
|
Kritika Joshi answered |
Length and Direction of Force Vector R
The force vector R is a fundamental concept in physics and engineering. It represents a force acting on an object and has both a length and a specific direction. The correct answer is option 'A', which states that the force vector R has a length equal to the magnitude of the force and a specific direction.
Length of R:
The length of the force vector R represents the magnitude or strength of the force. It is a scalar quantity and is usually measured in units such as Newtons (N) or pounds (lb). The length of R can be determined by measuring the force using appropriate instruments like force gauges or load cells. For example, if a force of 10 N is acting on an object, the length of vector R would be 10 units.
Direction of R:
The direction of the force vector R indicates the orientation or line of action of the force. It is a vector quantity and can be represented using various methods such as angles, coordinate systems, or Cartesian coordinates. The direction of R can be determined by using reference points or coordinate systems. For example, if a force is acting vertically downwards, the direction of vector R would be downwards.
Representation of R:
The force vector R can be represented graphically using arrows or vectors. The length of the arrow represents the magnitude of the force, and the direction of the arrow indicates the direction of the force. The vector R can also be represented mathematically using components or coordinates. In a two-dimensional Cartesian coordinate system, the vector R can be expressed as R = (Rx, Ry), where Rx and Ry are the components of the force vector along the x and y axes, respectively.
Significance of Length and Direction:
The length and direction of the force vector R are crucial in understanding and analyzing the effects of forces on objects. The length of R determines the strength of the force, while the direction of R determines the net effect of multiple forces acting on an object. By considering the length and direction of R, engineers and physicists can calculate various parameters such as the resultant force, equilibrium conditions, and motion of objects.
In conclusion, the force vector R has a length equal to the magnitude of the force and a specific direction. This understanding of the length and direction of R is essential for accurately representing and analyzing forces in physics and engineering.
The force vector R is a fundamental concept in physics and engineering. It represents a force acting on an object and has both a length and a specific direction. The correct answer is option 'A', which states that the force vector R has a length equal to the magnitude of the force and a specific direction.
Length of R:
The length of the force vector R represents the magnitude or strength of the force. It is a scalar quantity and is usually measured in units such as Newtons (N) or pounds (lb). The length of R can be determined by measuring the force using appropriate instruments like force gauges or load cells. For example, if a force of 10 N is acting on an object, the length of vector R would be 10 units.
Direction of R:
The direction of the force vector R indicates the orientation or line of action of the force. It is a vector quantity and can be represented using various methods such as angles, coordinate systems, or Cartesian coordinates. The direction of R can be determined by using reference points or coordinate systems. For example, if a force is acting vertically downwards, the direction of vector R would be downwards.
Representation of R:
The force vector R can be represented graphically using arrows or vectors. The length of the arrow represents the magnitude of the force, and the direction of the arrow indicates the direction of the force. The vector R can also be represented mathematically using components or coordinates. In a two-dimensional Cartesian coordinate system, the vector R can be expressed as R = (Rx, Ry), where Rx and Ry are the components of the force vector along the x and y axes, respectively.
Significance of Length and Direction:
The length and direction of the force vector R are crucial in understanding and analyzing the effects of forces on objects. The length of R determines the strength of the force, while the direction of R determines the net effect of multiple forces acting on an object. By considering the length and direction of R, engineers and physicists can calculate various parameters such as the resultant force, equilibrium conditions, and motion of objects.
In conclusion, the force vector R has a length equal to the magnitude of the force and a specific direction. This understanding of the length and direction of R is essential for accurately representing and analyzing forces in physics and engineering.
What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?
- a)It is either in the 1st quadrant or in 2nd quadrant
- b)It is either in the 1st quadrant or in 3rd quadrant
- c)It is either in the 1st quadrant or in 4th quadrant
- d)Only in the 1st quadrant
Correct answer is option 'C'. Can you explain this answer?
What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?
a)
It is either in the 1st quadrant or in 2nd quadrant
b)
It is either in the 1st quadrant or in 3rd quadrant
c)
It is either in the 1st quadrant or in 4th quadrant
d)
Only in the 1st quadrant
|
Swara Dasgupta answered |
If one is heading towards positive X-axis and the other is in the other direction opposite to the first one, with both having the same length and having an angle between them being obtuse, means that the direction is to be in the direction of either 1st quadrant or in the 4th quadrant.
A force vector with magnitude R and making an angle α with the x-axis is having its component along x-axis and y-axis as:- a)Rcosine (α) and Rsine(α)
- b)Rcosine (180-α) and Rsine(α)
- c)Rcosine (180-α) and Rsine(180+α)
- d)Rcosine (α) and Rsine(180+α)
Correct answer is option 'A'. Can you explain this answer?
A force vector with magnitude R and making an angle α with the x-axis is having its component along x-axis and y-axis as:
a)
Rcosine (α) and Rsine(α)
b)
Rcosine (180-α) and Rsine(α)
c)
Rcosine (180-α) and Rsine(180+α)
d)
Rcosine (α) and Rsine(180+α)
|
Sanskriti Basu answered |
The component along x-axis is the cosine component of the vector. And the y-axis component of the vector is sine component, if the angle is being made with the x-axis. And 180- α for some of the trigonometric function may change their sign.
If a vector is multiplied by a scalar:- a)Then its magnitude is increased by the square root of that scalar’s magnitude
- b)Then its magnitude is increased by the square of that scalar’s magnitude
- c)Then its magnitude is increased by amount of that scalar’s magnitude
- d)You cannot multiply the vector with a scalar
Correct answer is option 'C'. Can you explain this answer?
If a vector is multiplied by a scalar:
a)
Then its magnitude is increased by the square root of that scalar’s magnitude
b)
Then its magnitude is increased by the square of that scalar’s magnitude
c)
Then its magnitude is increased by amount of that scalar’s magnitude
d)
You cannot multiply the vector with a scalar
|
Anjali Sengupta answered |
If a vector is multiplied by a scalar then its magnitude is increased by amount of that scalar’s magnitude. When multiplied by a negative scalar it going to change the directional sense of the vector.
The resultant force acting, of the uniformly distributed loading is dependent on:- a)Area
- b)Vertical distance
- c)Length of the supports
- d)The distance of the supports between them
Correct answer is option 'A'. Can you explain this answer?
The resultant force acting, of the uniformly distributed loading is dependent on:
a)
Area
b)
Vertical distance
c)
Length of the supports
d)
The distance of the supports between them
|
|
Gopal Choudhury answered |
The resultant force acting, of the uniformly distributed loading is dependent on the area that the distribution is covering. The more the area the more is the force. That is the more is the tension created over the structure on which loading is kept. Hence the answer.
Which of the following statement is true?- a)A scalar is any physical quantity that can be completely specified by its magnitude
- b)A vector is any positive or negative physical quantity that can be completely specified by its magnitude
- c)A scalar is any physical quantity that requires both a magnitude and a direction for its complete description
- d)A scalar is any physical quantity that can be completely specified by its direction
Correct answer is option 'A'. Can you explain this answer?
Which of the following statement is true?
a)
A scalar is any physical quantity that can be completely specified by its magnitude
b)
A vector is any positive or negative physical quantity that can be completely specified by its magnitude
c)
A scalar is any physical quantity that requires both a magnitude and a direction for its complete description
d)
A scalar is any physical quantity that can be completely specified by its direction
|
Sravya Rane answered |
A scalar is any positive or negative physical quantity that can be completely specified by its magnitude. Examples of scalar quantities include length, mass, time, etc.
In case of forces, a couple means- a)Two unequal forces acting at two points
- b)Two equal and like parallel forces acting at two points
- c)Two equal and perpendicular forces acting at two points
- d)Two equal and opposite forces acting at two points
Correct answer is option 'D'. Can you explain this answer?
In case of forces, a couple means
a)
Two unequal forces acting at two points
b)
Two equal and like parallel forces acting at two points
c)
Two equal and perpendicular forces acting at two points
d)
Two equal and opposite forces acting at two points
|
Avinash Sharma answered |
Couple: When the pair of equal parallel forces that are opposite in direction applied on a body then it rotates of tries to rotate about a point or axis is called a couple.
Moment of a couple or couple (C) = P × a
Characteristics of a couple: A couple (whether clockwise or anticlockwise) has the following characteristics:
Moment of a couple or couple (C) = P × a
Characteristics of a couple: A couple (whether clockwise or anticlockwise) has the following characteristics:
- The algebraic sum of the forces, constituting the couple, is zero.
- The algebraic sum of the moments of the forces, constituting the couple, about any point is the same, and equal to the moment of the couple itself.
- A couple cannot be balanced by a single force. But it can be balanced only by a couple of opposite sense.
- Any no. of co-planer couples can be reduced to a single couple, whose magnitude will be equal to the algebraic sum of the moments of all the couples.
Torque (τ): It is a physical quantity, similar to force that causes the rotational motion. It is the cross product of the force with the perpendicular distance between the axis of rotation and the point of application of the force with the force.
⇒ τ = r × F = r F sin θ
Where r = distance from point of application of force (in meter), f = force (in Newton), and θ = angle between
Also, Torque (τ) = r × f = r × F
Where r = component of the distance in the direction perpendicular to the
F = component of the force in the direction perpendicular to
⇒ τ = r × F = r F sin θ
Where r = distance from point of application of force (in meter), f = force (in Newton), and θ = angle between
Also, Torque (τ) = r × f = r × F
Where r = component of the distance in the direction perpendicular to the
F = component of the force in the direction perpendicular to
What is multiplication law?- a)A.B =B.A
- b)a(A.B) = A.(aB)
- c)A.(B+D) = (A.B) + (A.D)
- d)a(A.B) = AxB
Correct answer is option 'B'. Can you explain this answer?
What is multiplication law?
a)
A.B =B.A
b)
a(A.B) = A.(aB)
c)
A.(B+D) = (A.B) + (A.D)
d)
a(A.B) = AxB
|
|
Gopal Choudhury answered |
For three vectors A, B and D the various laws are. Communitive law: A.B =B.A. While distributive law is A.(B+D) = (A.B) + (A.D). And multiplication law is a(A.B) = A.(aB).
Which of the following is correct? (For A representing the vector representation of the axis of rotation, r the radius vector and F the force vector)- a)A.(rxF)
- b)Ax(rxF)
- c)A.(r.F)
- d)Fx(r.F)
Correct answer is option 'A'. Can you explain this answer?
Which of the following is correct? (For A representing the vector representation of the axis of rotation, r the radius vector and F the force vector)
a)
A.(rxF)
b)
Ax(rxF)
c)
A.(r.F)
d)
Fx(r.F)
|
Suyash Patel answered |
The correct form of the equation is given by A.(rxF). Where A represents the vector representation of the axis of rotation, r the radius vector and F the force vector. This is usually done for determining the moment of the force about the axis. That is if body is being rotated by the force about an axis.
Determine the magnitude of the resultant force acting on the shaft shown from left.
- a)640N
- b)675N
- c)620N
- d)610N
Correct answer is option 'B'. Can you explain this answer?
Determine the magnitude of the resultant force acting on the shaft shown from left.
a)
640N
b)
675N
c)
620N
d)
610N
|
Akshara Rane answered |
The net force will act at the centroid of the parabola. Whether it be a parabola or the cubic curve the centroid is the only point at which the net force act. Force can’t be acted horizontally if the loading is vertical. Hence whatever be the shape of the loading, the centroid is the point of action of net force.
The magnitude of the resultant of the two vectors is always_____________- a)Greater than one of the vector’s magnitude
- b)Smaller than one of the vector’s magnitude
- c)Depends on the angle between them
- d)Axis we choose to calculate the magnitude
Correct answer is option 'C'. Can you explain this answer?
The magnitude of the resultant of the two vectors is always_____________
a)
Greater than one of the vector’s magnitude
b)
Smaller than one of the vector’s magnitude
c)
Depends on the angle between them
d)
Axis we choose to calculate the magnitude
|
Sinjini Bose answered |
Yes, the magnitude of the resultant of the two vectors always depends on the angle between them. It might be greater or smaller than one of the vector’s length. For perfectly saying, it does depends upon the angle between them.
Which statement is true? (For three vectors P, Q and R)- a)Associative law for cross product: (PxQ)xS = Px(QxS)
- b)Associative law for cross product: (PxQ)xS ≠ Px(QxS)
- c)Associative law for cross product: (PxQ)xS > Px(QxS)
- d)Associative law for cross product: (PxQ)xS < Px(QxS)
Correct answer is option 'B'. Can you explain this answer?
Which statement is true? (For three vectors P, Q and R)
a)
Associative law for cross product: (PxQ)xS = Px(QxS)
b)
Associative law for cross product: (PxQ)xS ≠ Px(QxS)
c)
Associative law for cross product: (PxQ)xS > Px(QxS)
d)
Associative law for cross product: (PxQ)xS < Px(QxS)
|
|
Shreya Kulkarni answered |
= Qx(PxS)c)Associative law for cross product: (PxQ)xS = (PxS)xQ
The resultant force is equal to the _______ of all the forces.- a)Sum
- b)Product
- c)Subtraction
- d)Division
Correct answer is option 'A'. Can you explain this answer?
The resultant force is equal to the _______ of all the forces.
a)
Sum
b)
Product
c)
Subtraction
d)
Division
|
|
Sanskriti Basu answered |
As the simplification means addition and the subtraction of the forces. This results in the simplification of the forces and thus gives us a single force. It is in a particular direction. But if one is considering the direction with the magnitude of the force, we can say that the resultant is the sum of all the forces.
The difference between the two types of loading namely uniformly distributed and the non-uniformly distributed loading is that:- a)The latter has the involvement of the integration for the calculation of the net force
- b)The former has the involvement of the integration for the calculation of the net force
- c)The latter has the involvement of the differentiation for the calculation of the net force
- d)The former has the involvement of the differentiation for the calculation of the net force
Correct answer is option 'A'. Can you explain this answer?
The difference between the two types of loading namely uniformly distributed and the non-uniformly distributed loading is that:
a)
The latter has the involvement of the integration for the calculation of the net force
b)
The former has the involvement of the integration for the calculation of the net force
c)
The latter has the involvement of the differentiation for the calculation of the net force
d)
The former has the involvement of the differentiation for the calculation of the net force
|
|
Sanskriti Chakraborty answered |
The non-uniformly distributed loading is using the integration for getting the net force given by it. And the former only need the area or the linear distance of the loading. That is when the distance is multiplied by the uniformly distributed load the net force is obtained. But that is not so with the non-uniform one.
Moments can be added like scalars that is it can be added algebraically with proper signs.- a)True
- b)False
Correct answer is option 'A'. Can you explain this answer?
Moments can be added like scalars that is it can be added algebraically with proper signs.
a)
True
b)
False
|
|
Disha Nambiar answered |
The moments in the 2D can be added algebraically just like the scalar quantities. But the need is that the signs must be taken into the consideration. As if clockwise is positive, so anti clockwise is negative. And the result can be negative too. That is counter clockwise direction.
The resultant couple moment is ____________ sum of various couples acting on the body.- a)Vector
- b)Scalar
- c)Scalar Triple
- d)Dot
Correct answer is option 'A'. Can you explain this answer?
The resultant couple moment is ____________ sum of various couples acting on the body.
a)
Vector
b)
Scalar
c)
Scalar Triple
d)
Dot
|
|
Sanskriti Basu answered |
As we know that the moment is vector quantity, their summation requires vector math. The couple moment is also the same. That is they are also the vectors, and requires vector math. Thus the resultant couple moment is the vector sum of the various couples acting in the body.
What if the perpendicular distance from the axis is infinity?- a)The rotation is not possible
- b)The rotation is possible but the moment generated is very less
- c)The force applied will be very much high for even a small rotation
- d)No rotation unless the contact is being broken
Correct answer is option 'C'. Can you explain this answer?
What if the perpendicular distance from the axis is infinity?
a)
The rotation is not possible
b)
The rotation is possible but the moment generated is very less
c)
The force applied will be very much high for even a small rotation
d)
No rotation unless the contact is being broken
|
|
Aniket Saini answered |
The long distance means a huge force which one needs to apply. Because distance increased will also increase the resistance inertia which will obviously increase the force required for the rotation. Though we know that the larger the distance the small is the force applied for rotation. But inertia must be taken into the considerations some times.
Determine the location of the resultant force acting on the shaft shown from left. The length is 2m.
- a)1.5m
- b)0.5m
- c)0.7m
- d)1.8m
Correct answer is option 'A'. Can you explain this answer?
Determine the location of the resultant force acting on the shaft shown from left. The length is 2m.
a)
1.5m
b)
0.5m
c)
0.7m
d)
1.8m
|
|
Stuti Bajaj answered |
The net force will act at the centroid of the parabola. Whether it be a parabola or the cubic curve the centroid is the only point at which the net force act. Force can’t be acted horizontally if the loading is vertical. Hence whatever be the shape of the loading, the centroid is the point of action of net force.
If you are getting to know about the direction of the moment caused by the force applied on the body by using your wrist and curling it in the direction of the rotation then which of the following is not right?
- a)The thumb represents the direction of the moment
- b)The thumb represents the direction of the force
- c)The fingers represents the direction of the force
- d)The direction in which you curl your wrist is towards the direction of the distance from point of contact of force to the axis of rotation.
Correct answer is option 'B'. Can you explain this answer?
If you are getting to know about the direction of the moment caused by the force applied on the body by using your wrist and curling it in the direction of the rotation then which of the following is not right?
a)
The thumb represents the direction of the moment
b)
The thumb represents the direction of the force
c)
The fingers represents the direction of the force
d)
The direction in which you curl your wrist is towards the direction of the distance from point of contact of force to the axis of rotation.
|
Arshiya Dey answered |
The curled hand represents various thing. The direction of the moment axis is given by the thumb. The direction of the force is given by the fingers. As we place the fingers on the force and curl towards the rotational direction of the body about the axis.
In the equation A.(rxF) the r is heading from ______________ and ending at _____________- a)Axis of rotation, Force vector
- b)Axis of rotation, Force vector’s point of action on the body
- c)Force vector, Axis of rotation
- d)Force vector’s point of action on the body, Axis of rotation
Correct answer is option 'B'. Can you explain this answer?
In the equation A.(rxF) the r is heading from ______________ and ending at _____________
a)
Axis of rotation, Force vector
b)
Axis of rotation, Force vector’s point of action on the body
c)
Force vector, Axis of rotation
d)
Force vector’s point of action on the body, Axis of rotation
|
|
Saranya Saha answered |
It is the radius vector. The radius vector is always from the axis of rotation to the point of action of the force on the body. Which means that the radius vector is not on any point on the force vector. Rather it ending at the point on the force vector, where it is being in contact of the body.
If a car is moving forward, what is the direction of the moment of the moment caused by the rotation of the tires?- a)It is heading inwards, i.e. the direction is towards inside of the car
- b)It is heading outwards, i.e. the direction is towards outside of the car
- c)It is heading forward, i.e. the direction is towards the forward direction of the motion of the car
- d)It is heading backward, i.e. the direction is towards back side of the motion of the car
Correct answer is option 'A'. Can you explain this answer?
If a car is moving forward, what is the direction of the moment of the moment caused by the rotation of the tires?
a)
It is heading inwards, i.e. the direction is towards inside of the car
b)
It is heading outwards, i.e. the direction is towards outside of the car
c)
It is heading forward, i.e. the direction is towards the forward direction of the motion of the car
d)
It is heading backward, i.e. the direction is towards back side of the motion of the car
|
|
Disha Nambiar answered |
When you curl your wrist in the direction in which the tires are moving then you will find that the thumb is pointing outwards. That is outwards the body of the car. This phenomena is also observed in rainy seasons. When cars travel on the roads, the water is thrown outside from the tires, due to moment.
The moment axis, force and the perpendicular distance in the moment of the force calculation is lying in____________- a)Two planes perpendicular to each other
- b)A single plane in the direction of the force
- c)A single plane in the direction of the perpendicular distance
- d)A single line in the direction of the force
Correct answer is option 'A'. Can you explain this answer?
The moment axis, force and the perpendicular distance in the moment of the force calculation is lying in____________
a)
Two planes perpendicular to each other
b)
A single plane in the direction of the force
c)
A single plane in the direction of the perpendicular distance
d)
A single line in the direction of the force
|
|
Jyoti Deshpande answered |
The moment axis, force and the perpendicular distance is lying in the three dimensional Cartesian. It doesn’t lye on the single plane. It also doesn’t lye in a single line. Nor in the direction of the force. Thus they all lye in the planes which are perpendicular to each other.
Which is true for two vector A = A1i + A2j + A3k and B = B1i + B2j + B3k?- a)A.B = A1B1 + A2B2 + A3B3
- b)AxB = A1B1 + A2B2 + A3B3
- c)A.B = A1B2 + A2B3 + A3B1
- d)AxB = A1B2 + A2B3 + A3B1
Correct answer is option 'A'. Can you explain this answer?
Which is true for two vector A = A1i + A2j + A3k and B = B1i + B2j + B3k?
a)
A.B = A1B1 + A2B2 + A3B3
b)
AxB = A1B1 + A2B2 + A3B3
c)
A.B = A1B2 + A2B3 + A3B1
d)
AxB = A1B2 + A2B3 + A3B1
|
|
Devansh Sengupta answered |
The multiplication of x, y and z components with their respective same component give a scalar, equal to 1, i.e. i.i = 1 and j.j = 1, while jxj =0. This is the basic principle of the vector algebra which needs to apply wherever needed.
A man is travelling in the car. He is driving the car. If he is taking a turn in the road. He is applying force to the steering wheel by holding the wheel with his both hands. The steering wheel is facing a moment of force.- a)True
- b)False
Correct answer is option 'B'. Can you explain this answer?
A man is travelling in the car. He is driving the car. If he is taking a turn in the road. He is applying force to the steering wheel by holding the wheel with his both hands. The steering wheel is facing a moment of force.
a)
True
b)
False
|
|
Aman Ghosh answered |
Explanation:
The correct answer is option B: False. The statement is incorrect because taking a turn in the road does not involve applying a moment of force to the steering wheel.
Steering Wheel and Force:
The steering wheel is a component of a car's steering system that allows the driver to control the direction of the vehicle. It is connected to the front wheels through a series of linkages and mechanisms. When the driver turns the steering wheel, it causes the front wheels to change their orientation, which in turn changes the direction of the car.
Force and Moment of Force:
Force is a vector quantity that is defined as a push or pull that can cause an object with mass to accelerate or change its state of motion. It is measured in newtons (N). A moment of force, also known as torque, is a measure of the tendency of a force to rotate an object about an axis. It is calculated by multiplying the force applied by the perpendicular distance from the axis of rotation.
Applying Force to the Steering Wheel:
When a driver takes a turn in a car, they apply a force to the steering wheel. However, this force is not a moment of force or torque. Instead, it is a linear force that is applied along the circumference of the steering wheel. The driver uses their hands to push or pull on the steering wheel, causing it to rotate. This rotation is then transmitted to the front wheels, causing them to turn and change the direction of the car.
Conclusion:
In conclusion, when a driver takes a turn in a car, they apply a linear force to the steering wheel, not a moment of force. Therefore, the statement that the steering wheel is facing a moment of force when the driver takes a turn is false.
The correct answer is option B: False. The statement is incorrect because taking a turn in the road does not involve applying a moment of force to the steering wheel.
Steering Wheel and Force:
The steering wheel is a component of a car's steering system that allows the driver to control the direction of the vehicle. It is connected to the front wheels through a series of linkages and mechanisms. When the driver turns the steering wheel, it causes the front wheels to change their orientation, which in turn changes the direction of the car.
Force and Moment of Force:
Force is a vector quantity that is defined as a push or pull that can cause an object with mass to accelerate or change its state of motion. It is measured in newtons (N). A moment of force, also known as torque, is a measure of the tendency of a force to rotate an object about an axis. It is calculated by multiplying the force applied by the perpendicular distance from the axis of rotation.
Applying Force to the Steering Wheel:
When a driver takes a turn in a car, they apply a force to the steering wheel. However, this force is not a moment of force or torque. Instead, it is a linear force that is applied along the circumference of the steering wheel. The driver uses their hands to push or pull on the steering wheel, causing it to rotate. This rotation is then transmitted to the front wheels, causing them to turn and change the direction of the car.
Conclusion:
In conclusion, when a driver takes a turn in a car, they apply a linear force to the steering wheel, not a moment of force. Therefore, the statement that the steering wheel is facing a moment of force when the driver takes a turn is false.
The couple is a scalar quantity and the force is vector quantity and hence only force can be simplified as _____- a)The first part of the statement is false and another part is true
- b)The first part of the statement is false and another part is false too
- c)The first part of the statement is true and another part is false
- d)The first part of the statement is true and another part is true too
Correct answer is option 'A'. Can you explain this answer?
The couple is a scalar quantity and the force is vector quantity and hence only force can be simplified as _____
a)
The first part of the statement is false and another part is true
b)
The first part of the statement is false and another part is false too
c)
The first part of the statement is true and another part is false
d)
The first part of the statement is true and another part is true too
|
|
Hiral Jain answered |
Explanation:
The given statement states that "The couple is a scalar quantity and the force is a vector quantity, and hence only force can be simplified."
To determine the correctness of this statement, we need to understand the definitions and properties of both couple and force.
1. Couple:
A couple is a system of forces that act on a body but do not have a resultant force or a resultant moment about any point. It consists of two parallel forces with equal magnitudes and opposite directions, but they are not collinear. The magnitude of the couple is given by the product of one of the forces and the perpendicular distance between the forces.
2. Force:
A force is a vector quantity that has both magnitude and direction. It can be represented by an arrow, where the length of the arrow represents the magnitude of the force and the direction of the arrow represents the direction of the force.
Explanation of the given statement:
The given statement states that the couple is a scalar quantity and the force is a vector quantity. However, this statement is incorrect. Here's why:
1. Couple is not a scalar quantity:
A couple cannot be considered a scalar quantity because it has both magnitude (product of force and distance) and direction (perpendicular to the plane in which the forces act). Therefore, the first part of the statement is false.
2. Force is a vector quantity:
This part of the statement is true. A force is a vector quantity as it possesses both magnitude and direction. It follows the laws of vector addition and subtraction. Forces can be added using vector addition, and their resultant can be determined.
Conclusion:
Based on the explanations provided above, we can conclude that the correct answer is option 'A': The first part of the statement is false, and the second part is true. The couple is not a scalar quantity, and the force is a vector quantity.
The given statement states that "The couple is a scalar quantity and the force is a vector quantity, and hence only force can be simplified."
To determine the correctness of this statement, we need to understand the definitions and properties of both couple and force.
1. Couple:
A couple is a system of forces that act on a body but do not have a resultant force or a resultant moment about any point. It consists of two parallel forces with equal magnitudes and opposite directions, but they are not collinear. The magnitude of the couple is given by the product of one of the forces and the perpendicular distance between the forces.
2. Force:
A force is a vector quantity that has both magnitude and direction. It can be represented by an arrow, where the length of the arrow represents the magnitude of the force and the direction of the arrow represents the direction of the force.
Explanation of the given statement:
The given statement states that the couple is a scalar quantity and the force is a vector quantity. However, this statement is incorrect. Here's why:
1. Couple is not a scalar quantity:
A couple cannot be considered a scalar quantity because it has both magnitude (product of force and distance) and direction (perpendicular to the plane in which the forces act). Therefore, the first part of the statement is false.
2. Force is a vector quantity:
This part of the statement is true. A force is a vector quantity as it possesses both magnitude and direction. It follows the laws of vector addition and subtraction. Forces can be added using vector addition, and their resultant can be determined.
Conclusion:
Based on the explanations provided above, we can conclude that the correct answer is option 'A': The first part of the statement is false, and the second part is true. The couple is not a scalar quantity, and the force is a vector quantity.
Which among the following is the distributive law for the cross product of three vectors?- a)Px(Q+S) = (PxQ) + (PxS)
- b)Px(QxS) = (PxQ) + (PxS)
- c)Px(QxS) = (PxQ) x (PxS)
- d)Px(Q+S) = (PxQ) + (QxS)
Correct answer is option 'A'. Can you explain this answer?
Which among the following is the distributive law for the cross product of three vectors?
a)
Px(Q+S) = (PxQ) + (PxS)
b)
Px(QxS) = (PxQ) + (PxS)
c)
Px(QxS) = (PxQ) x (PxS)
d)
Px(Q+S) = (PxQ) + (QxS)
|
Ashwin Desai answered |
Explanation:
Distributive law for the cross product of three vectors:
The distributive law for the cross product of three vectors states that the cross product of the first vector with the sum of the second and third vectors is equal to the sum of the cross products of the first vector with the second vector and the first vector with the third vector.
Explanation of option 'A':
In the given options, option 'A' represents the distributive law for the cross product of three vectors.
- Px(Q+S) = (PxQ) + (PxS)
- This equation shows that the cross product of vector P with the sum of vectors Q and S is equal to the sum of the cross products of vector P with vector Q and vector P with vector S.
Therefore, option 'A' is the correct choice for the distributive law for the cross product of three vectors.
Distributive law for the cross product of three vectors:
The distributive law for the cross product of three vectors states that the cross product of the first vector with the sum of the second and third vectors is equal to the sum of the cross products of the first vector with the second vector and the first vector with the third vector.
Explanation of option 'A':
In the given options, option 'A' represents the distributive law for the cross product of three vectors.
- Px(Q+S) = (PxQ) + (PxS)
- This equation shows that the cross product of vector P with the sum of vectors Q and S is equal to the sum of the cross products of vector P with vector Q and vector P with vector S.
Therefore, option 'A' is the correct choice for the distributive law for the cross product of three vectors.
If the rotation is clockwise in this page, suppose, then in which direction will the thumb project if you curl your hand in the same direction of the rotation?- a)It will point to the direction perpendicular to the plane of paper and towards you
- b)It will point to the direction perpendicular to the plane of paper and away from you
- c)It will point to the direction parallel to the plane of paper and towards right
- d)It will point to the direction parallel to the plane of paper and towards left
Correct answer is option 'B'. Can you explain this answer?
If the rotation is clockwise in this page, suppose, then in which direction will the thumb project if you curl your hand in the same direction of the rotation?
a)
It will point to the direction perpendicular to the plane of paper and towards you
b)
It will point to the direction perpendicular to the plane of paper and away from you
c)
It will point to the direction parallel to the plane of paper and towards right
d)
It will point to the direction parallel to the plane of paper and towards left
|
|
Amrita Chauhan answered |
As the curling will give the direction perpendicular to the paper. But it does depend upon the rotation sense. In this example, the sense is clockwise. Thus the thumb goes into the paper. That is it goes away from the viewer. Thus the answer.
In the simplification of the loading system the net force acts at the ___________ of the loading body.- a)Centroid
- b)The centre axis
- c)The corner
- d)The base
Correct answer is option 'A'. Can you explain this answer?
In the simplification of the loading system the net force acts at the ___________ of the loading body.
a)
Centroid
b)
The centre axis
c)
The corner
d)
The base
|
|
Stuti Bajaj answered |
In the simplification of the loading system the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then the at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading.
Which of them is not correct?- a)j x j = 0
- b)j x k = i
- c)j x i = k
- d)j x i = -k
Correct answer is option 'C'. Can you explain this answer?
Which of them is not correct?
a)
j x j = 0
b)
j x k = i
c)
j x i = k
d)
j x i = -k
|
|
Mahi Kaur answered |
As asked, the one which is not correct is the third one. The product is containing the cosine function, and the angle which is going to be inserted in the function is the angle between the vectors. Thus if the angle is 90, then the cross will be zero.
Commutative law is valid for the cross product of two vectors. (Commutative law: PxQ = QxP; for two vectors P and Q)- a)True
- b)False
Correct answer is option 'B'. Can you explain this answer?
Commutative law is valid for the cross product of two vectors. (Commutative law: PxQ = QxP; for two vectors P and Q)
a)
True
b)
False
|
|
Divyansh Goyal answered |
The Commutative Law and the Cross Product of Vectors
The commutative law states that for any two elements, the order of the operation does not affect the result. In the case of vectors, this means that the order in which we perform the cross product should not affect the outcome. However, the correct answer to the given question is option 'B' - False. Let's understand why.
Explanation:
1. The Cross Product:
The cross product is an operation that combines two vectors to produce a third vector that is perpendicular to both of the original vectors. It is denoted by the symbol '×' and is defined as:
P × Q = ||P|| ||Q|| sin(θ) n
where P and Q are the vectors being crossed, ||P|| and ||Q|| are their magnitudes, θ is the angle between them, and n is a unit vector perpendicular to the plane formed by P and Q.
2. Commutative Law:
The commutative law states that for any two elements, the order of the operation does not affect the result. In mathematical terms, it can be written as:
a × b = b × a
This law holds true for many mathematical operations, such as addition and multiplication. However, it does not hold true for the cross product of vectors.
3. Non-Commutativity of Cross Product:
The cross product of vectors is not commutative, which means that changing the order of the vectors being crossed will result in a different outcome.
To see this, let's consider two vectors P and Q. The cross product of P and Q is given by:
P × Q = ||P|| ||Q|| sin(θ) n
Now, if we switch the order and calculate the cross product of Q and P, we get:
Q × P = ||Q|| ||P|| sin(θ') n'
Here, θ' is the angle between Q and P, and n' is a unit vector perpendicular to the plane formed by Q and P.
Since the angles and magnitudes may be different for P and Q, the resulting cross products will also be different. Thus, the commutative law does not hold for the cross product of vectors.
Conclusion:
In conclusion, the commutative law is not valid for the cross product of two vectors. The order of the vectors being crossed affects the outcome, and switching the order will result in a different cross product.
The commutative law states that for any two elements, the order of the operation does not affect the result. In the case of vectors, this means that the order in which we perform the cross product should not affect the outcome. However, the correct answer to the given question is option 'B' - False. Let's understand why.
Explanation:
1. The Cross Product:
The cross product is an operation that combines two vectors to produce a third vector that is perpendicular to both of the original vectors. It is denoted by the symbol '×' and is defined as:
P × Q = ||P|| ||Q|| sin(θ) n
where P and Q are the vectors being crossed, ||P|| and ||Q|| are their magnitudes, θ is the angle between them, and n is a unit vector perpendicular to the plane formed by P and Q.
2. Commutative Law:
The commutative law states that for any two elements, the order of the operation does not affect the result. In mathematical terms, it can be written as:
a × b = b × a
This law holds true for many mathematical operations, such as addition and multiplication. However, it does not hold true for the cross product of vectors.
3. Non-Commutativity of Cross Product:
The cross product of vectors is not commutative, which means that changing the order of the vectors being crossed will result in a different outcome.
To see this, let's consider two vectors P and Q. The cross product of P and Q is given by:
P × Q = ||P|| ||Q|| sin(θ) n
Now, if we switch the order and calculate the cross product of Q and P, we get:
Q × P = ||Q|| ||P|| sin(θ') n'
Here, θ' is the angle between Q and P, and n' is a unit vector perpendicular to the plane formed by Q and P.
Since the angles and magnitudes may be different for P and Q, the resulting cross products will also be different. Thus, the commutative law does not hold for the cross product of vectors.
Conclusion:
In conclusion, the commutative law is not valid for the cross product of two vectors. The order of the vectors being crossed affects the outcome, and switching the order will result in a different cross product.
What is the dot product of two vectors which are having magnitude equal to unity and are making an angle of 45°?- a)0.707
- b)-0.707
- c)1.414
- d)-1.414
Correct answer is option 'A'. Can you explain this answer?
What is the dot product of two vectors which are having magnitude equal to unity and are making an angle of 45°?
a)
0.707
b)
-0.707
c)
1.414
d)
-1.414
|
Asha Nambiar answered |
°
The dot product of two vectors is given by the product of their magnitudes and the cosine of the angle between them.
Let's assume the two vectors as a and b.
Magnitude of vector a = 1
Magnitude of vector b = 1
Angle between them = 45°
Therefore, the dot product of vectors a and b can be calculated as:
a · b = |a| |b| cos θ
a · b = (1)(1) cos 45°
a · b = (1)(1) (1/√2)
a · b = 1/√2
Hence, the dot product of two vectors having magnitude equal to unity and making an angle of 45° is 1/√2.
The dot product of two vectors is given by the product of their magnitudes and the cosine of the angle between them.
Let's assume the two vectors as a and b.
Magnitude of vector a = 1
Magnitude of vector b = 1
Angle between them = 45°
Therefore, the dot product of vectors a and b can be calculated as:
a · b = |a| |b| cos θ
a · b = (1)(1) cos 45°
a · b = (1)(1) (1/√2)
a · b = 1/√2
Hence, the dot product of two vectors having magnitude equal to unity and making an angle of 45° is 1/√2.
α = cos-1(A.B/AB). What is the range of α?- a)0˚<α<90˚
- b)0˚<α<180˚
- c)90˚<α<180C
- d)0˚<α<45˚
Correct answer is option 'B'. Can you explain this answer?
α = cos-1(A.B/AB). What is the range of α?
a)
0˚<α<90˚
b)
0˚<α<180˚
c)
90˚<α<180C
d)
0˚<α<45˚
|
|
Shruti Bose answered |
Cosine inverse function is defined only between 0˚ to 180˚. It cannot be defined under any of the given range, because this is the principle range of the inverse cosine function.
If any external force also is applied on the distributed loading then?- a)The net force will act at the centroid of the structure only
- b)The net load will not be formed as all the forces will be cancelled
- c)The net force will act on the base of the loading horizontally
- d)The net force will not to be considered, there would be a net force of the distribution, rest will be the external forces
Correct answer is option 'D'. Can you explain this answer?
If any external force also is applied on the distributed loading then?
a)
The net force will act at the centroid of the structure only
b)
The net load will not be formed as all the forces will be cancelled
c)
The net force will act on the base of the loading horizontally
d)
The net force will not to be considered, there would be a net force of the distribution, rest will be the external forces
|
|
Stuti Mishra answered |
The external forces are treated differently. They are not added by the force of the distributed loading. That is the force not only acts at the centroid always. It can be shifted also. Depending on the external forces.
Couple is having a combination of two forces. They are different in magnitude.- a)True
- b)False
Correct answer is option 'B'. Can you explain this answer?
Couple is having a combination of two forces. They are different in magnitude.
a)
True
b)
False
|
|
Pankaj Joshi answered |
The couple is a combination of two forces of same magnitude. They are acting in the same sense of rotation. That is they are acting in the opposite direction, but giving the body a rotation in the same direction. Whether it may be in clockwise direction or anti-clockwise.
Determine the magnitude of the force F = 300j parallel to the direction of AB?
- a)155N
- b)257.1N
- c)200N
- d)175N
Correct answer is option 'B'. Can you explain this answer?
Determine the magnitude of the force F = 300j parallel to the direction of AB?
a)
155N
b)
257.1N
c)
200N
d)
175N
|
|
Pranavi Gupta answered |
Force component in the direction parallel to the AB is given by unit vector 0.286i + 0.857j + 0.429k. Now (300j).(0.286i + 0.857j + 0.429k) = 257.1N. Just try to resolve the force into it’s particular components.
If the forces acting on the couple are in the same direction, that is they are not in the opposite direction as always they are, then?- a)The direction of the forces doesn’t determine the moment
- b)The couple moment will be maximum
- c)The couple is not possible
- d)No change occurs
Correct answer is option 'C'. Can you explain this answer?
If the forces acting on the couple are in the same direction, that is they are not in the opposite direction as always they are, then?
a)
The direction of the forces doesn’t determine the moment
b)
The couple moment will be maximum
c)
The couple is not possible
d)
No change occurs
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Meera Bose answered |
B) The direction of the forces does not matter for the couple's effect. The couple moment will still be the same.
The simplification of the couple is done on the basis of the ______________- a)The clockwise of the anti-clockwise rotation sign convention
- b)The simplification is not possible
- c)The couple is a vector and thus can’t be simplified
- d)The couple is a scalar and can’t be simplified
Correct answer is option 'A'. Can you explain this answer?
The simplification of the couple is done on the basis of the ______________
a)
The clockwise of the anti-clockwise rotation sign convention
b)
The simplification is not possible
c)
The couple is a vector and thus can’t be simplified
d)
The couple is a scalar and can’t be simplified
|
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Stuti Bajaj answered |
The couple is simplified by taking the direction of the rotation of the body as positive or negative. That is if the clockwise direction is positive then the anti-clockwise direction is taken as negative. If the couple is a vector it can be easily simplified by taking the components.
For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents:- a)Their magnitude’s square and direction of the line of action respectively
- b)Their magnitude and direction of the line of action respectively
- c)Magnitude’s square root and direction of the line of action respectively
- d)Magnitude’s square and ratio of their lengths respectively
Correct answer is option 'B'. Can you explain this answer?
For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents:
a)
Their magnitude’s square and direction of the line of action respectively
b)
Their magnitude and direction of the line of action respectively
c)
Magnitude’s square root and direction of the line of action respectively
d)
Magnitude’s square and ratio of their lengths respectively
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Sanskriti Basu answered |
For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents their magnitude and direction of the line of action respectively. The head/tip of the arrow indicates the sense of direction of the vector.
Find the moment along Q.
- a)1200Nm
- b)600Nm
- c)0Nm
- d)1400Nm
Correct answer is option 'A'. Can you explain this answer?
Find the moment along Q.
a)
1200Nm
b)
600Nm
c)
0Nm
d)
1400Nm
|
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Niharika Iyer answered |
As we know that the moment is the cross product of the distance and the force we will try to apply the same here. But here we have a number of forces components acting on the T point. So by adding all the moments caused by all the forces will give us the value as 600Nm.
Which of the following is true?- a)Total moment of various forces acting on the body is the vector sum of all moments
- b)Total moment of various forces acting on the body is the algebraic sum of all moments
- c)Total moment of various forces acting on the body is always zero
- d)Total moment of various forces acting on the body is the vector sum of all moments which is perpendicular to each other forces
Correct answer is option 'A'. Can you explain this answer?
Which of the following is true?
a)
Total moment of various forces acting on the body is the vector sum of all moments
b)
Total moment of various forces acting on the body is the algebraic sum of all moments
c)
Total moment of various forces acting on the body is always zero
d)
Total moment of various forces acting on the body is the vector sum of all moments which is perpendicular to each other forces
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Ameya Kaur answered |
The moment is the vector quantity. Thus the value of the total moment caused by various forces acting on the body is the vector sum of all the vectors. Also the moments are not perpendicular to each other, unless it is specified. Thus assumptions cant be taken for the direction of the moment.
A couple moment is a _______ vector.- a)Gradient
- b)Scalar
- c)Del
- d)Free
Correct answer is option 'D'. Can you explain this answer?
A couple moment is a _______ vector.
a)
Gradient
b)
Scalar
c)
Del
d)
Free
|
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Bhargavi Chauhan answered |
A couple moment is a free vector. It can be act anywhere between the forces. As the couple is formed by two forces acting in the opposite directions. These forces are separated by a distance r, say, then the moment caused by them can act anywhere in between these forces.
In the calculation of the moment of the force about the axis, the cross product table, i.e. the 3X3 matrix which is made for doing the cross product having 3 rows, contains three elements. Which are they from top to bottom?- a)Axis coordinates, point coordinates and the force coordinates
- b)Point coordinates, axis coordinates, and the force coordinates
- c)Axis coordinates, force coordinates and the point coordinates
- d)Force coordinates, point coordinates and the axis coordinates
Correct answer is option 'A'. Can you explain this answer?
In the calculation of the moment of the force about the axis, the cross product table, i.e. the 3X3 matrix which is made for doing the cross product having 3 rows, contains three elements. Which are they from top to bottom?
a)
Axis coordinates, point coordinates and the force coordinates
b)
Point coordinates, axis coordinates, and the force coordinates
c)
Axis coordinates, force coordinates and the point coordinates
d)
Force coordinates, point coordinates and the axis coordinates
|
Isha Bajaj answered |
The Cross Product and Moment of Force
The cross product is a mathematical operation that combines two vectors to produce a third vector that is perpendicular to both of the original vectors. In the context of mechanics, the cross product is often used to calculate the moment of a force about a given axis.
The Cross Product Table
When performing cross product calculations, a 3x3 matrix known as the cross product table is used. This matrix is made up of three rows and three columns, and each element represents a specific coordinate.
The elements of the cross product table are arranged in a specific order to ensure the correct calculation of the cross product. In the context of calculating the moment of a force about an axis, the elements in the cross product table represent the following:
- The first row represents the coordinates of the axis.
- The second row represents the coordinates of the point where the force is applied.
- The third row represents the coordinates of the force itself.
The Correct Order of Elements in the Cross Product Table
According to the question, the correct order of elements in the cross product table, from top to bottom, is:
a) Axis coordinates, point coordinates, and force coordinates
This means that the first row of the cross product table represents the coordinates of the axis, the second row represents the coordinates of the point where the force is applied, and the third row represents the coordinates of the force itself.
Why Option 'A' is the Correct Answer
The correct answer, option 'A', is derived from the correct order of elements in the cross product table. The order of the elements is crucial for correctly calculating the moment of a force about an axis. If the order is changed, the calculation will yield incorrect results.
Therefore, when calculating the moment of a force about an axis, it is essential to arrange the elements in the cross product table in the correct order, with the axis coordinates in the first row, the point coordinates in the second row, and the force coordinates in the third row.
The cross product is a mathematical operation that combines two vectors to produce a third vector that is perpendicular to both of the original vectors. In the context of mechanics, the cross product is often used to calculate the moment of a force about a given axis.
The Cross Product Table
When performing cross product calculations, a 3x3 matrix known as the cross product table is used. This matrix is made up of three rows and three columns, and each element represents a specific coordinate.
The elements of the cross product table are arranged in a specific order to ensure the correct calculation of the cross product. In the context of calculating the moment of a force about an axis, the elements in the cross product table represent the following:
- The first row represents the coordinates of the axis.
- The second row represents the coordinates of the point where the force is applied.
- The third row represents the coordinates of the force itself.
The Correct Order of Elements in the Cross Product Table
According to the question, the correct order of elements in the cross product table, from top to bottom, is:
a) Axis coordinates, point coordinates, and force coordinates
This means that the first row of the cross product table represents the coordinates of the axis, the second row represents the coordinates of the point where the force is applied, and the third row represents the coordinates of the force itself.
Why Option 'A' is the Correct Answer
The correct answer, option 'A', is derived from the correct order of elements in the cross product table. The order of the elements is crucial for correctly calculating the moment of a force about an axis. If the order is changed, the calculation will yield incorrect results.
Therefore, when calculating the moment of a force about an axis, it is essential to arrange the elements in the cross product table in the correct order, with the axis coordinates in the first row, the point coordinates in the second row, and the force coordinates in the third row.
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Engineering Mechanics for Mechanical Engineering
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