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All questions of Engineering Mechanics for Mechanical Engineering Exam

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Which of the following is an example of a body undergoing translational equilibrium?
  • a)
    A body at rest on a table
  • b)
    A body travelling in a circular path at a constant speed
  • c)
    A body rotating with constant angular speed about an axis
  • d)
    A body sliding down a frictionless inclined plane
Correct answer is option 'A'. Can you explain this answer?

Nisha Singh answered
An object is said to be in equilibrium when there is no external net force acting on it. When an object is in equilibrium, it does not accelerate. If it had a velocity, the velocity remains constant; if it was at rest, it remains at rest.
If all the forces acting on a particular object add up to zero and have no resultant force, then it’s in translational equilibrium. Examples would be a book resting on a bookshelf, or someone walking at a steady, constant speed.
An object that’s not rotating or doing so at a steady speed, the sum of the torques acting on it equaling zero, is at rotational equilibrium. Some examples of this are a Ferris wheel turning at a constant velocity, two children of equal weight balanced on either side of a seesaw, or the Earth rotating on its axis at a steady speed.

Which of the following conditions do not change the effect of couple?
  • a)
    Shifting of couple to a new position in its plane
  • b)
    Shifting of couple to a parallel plane
  • c)
    Rotation of couple in its plane
  • d)
    All of the above
Correct answer is option 'D'. Can you explain this answer?

Pritam Jain answered
Two parallel forces equal in magnitude and opposite in direction and separated by a definite distance are said to form a couple.
The translatory effect of a couple on the body is zero.
The only effect of a couple is a moment and this moment is same about any point, the effect of a couple is unchanged if:
(i) The couple is rotated through any plane
(ii) The couple is shifted to any other position
(iii) The couple is replaced by another pair of forces whose rotational effect is same

A beam is fixed at one end and is vertically supported at the other end. What is the degree of statical indeterminacy?
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'A'. Can you explain this answer?

Rounak Banerjee answered
The degree of statical indeterminacy of a structure refers to the number of unknown reactions or internal forces that cannot be determined by the equations of static equilibrium alone. It is an important concept in structural analysis to understand the behavior of a structure under loads.

In this particular case, we have a beam that is fixed at one end and vertically supported at the other end. Let's analyze the degree of statical indeterminacy for this beam.

1. Identify the support conditions:
- Fixed support at one end: This support prevents both translation and rotation of the beam.
- Vertical support at the other end: This support prevents only vertical translation of the beam.

2. Determine the number of unknown reactions:
- Fixed support at one end: This support generates three unknown reactions - vertical reaction, horizontal reaction, and moment reaction.
- Vertical support at the other end: This support generates one unknown reaction - vertical reaction.

3. Apply the equations of static equilibrium:
- For a two-dimensional structure like this beam, the equations of static equilibrium are:
- Sum of vertical forces = 0
- Sum of horizontal forces = 0
- Sum of moments = 0

4. Analyze the equations of static equilibrium:
- Sum of vertical forces: With one vertical reaction at the vertical support, we can determine this equation.
- Sum of horizontal forces: Since there are no horizontal external forces, this equation is automatically satisfied.
- Sum of moments: The fixed support at one end generates a moment reaction, but the vertical support at the other end does not generate any moment reaction. So, this equation is not applicable.

5. Conclusion:
- From the analysis, we can see that we have one unknown reaction (vertical reaction at the vertical support) and one equation (sum of vertical forces) to solve for it.
- Therefore, the degree of statical indeterminacy is 1.

So, the correct answer is option 'A' - 1.

Concurrent force system is the system when:
  • a)
    Lines of action of all forces pass through a point
  • b)
    Lines of action of all forces are parallel to each other
  • c)
    Lines of action of all forces lie along same line
  • d)
    Lines of action of all forces are not parallel to each other
Correct answer is option 'A'. Can you explain this answer?

Sagarika Mukherjee answered
Collinear Forces: Line of action of all the forces act along the same line.
Coplanar parallel forces: All forces are parallel to each other and lie in a single plane
Coplanar concurrent forces: Line of action of all forces pass through a single point and forces lie in the same plane
Coplanar non-concurrent forces: All forces do not meet at a point, but lie in a single plane
Non-coplanar parallel forces: All the forces are parallel to each other, but not in same plane
Non-coplanar concurrent forces: All forces do not lie in the same plane, but their lines of action pass through a single point
Non-coplanar non-concurrent forces: All forces do not lie in the same plane and their lines of action do not pass through a single point

In case of principal axes of a section _____.  
  • a)
    Sum of moment of inertia is zero
  • b)
    Difference of moment of inertia is zero
  • c)
    Product of moment of inertia is zero
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Sagarika Dey answered
In principal axes of a section product of inertia is zero.
Product of inertia:- The moment of inertia between any two mutually perpendicular axis in the plane of area is the produce of inertia.
Product of inertia,
Ixy=∫dA.xy

A fan consumes 20 W of electric power and discharges air from a ventilated room at 0.25 kg/s. The maximum air outlet velocity is nearly 
  • a)
    4.7 m/s
  • b)
    8.7 m/s
  • c)
    10.2 m/s
  • d)
    12.7 m/s
Correct answer is option 'D'. Can you explain this answer?

Sagarika Dey answered
A fan is claimed to increase the velocity of air to a specified value while consuming electric power at a specified rate. The electric power input will be equal to the rate of increase of the kinetic energy of air

The Force applied on a body of mass 100 kg to produce an acceleration of 5 m/s2, is
  • a)
    20 N
  • b)
    100 N
  • c)
    500 N
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Ameya Kaur answered
Mass and Acceleration

Mass:
Mass is a fundamental property of matter that measures the amount of matter in an object. It is a scalar quantity and is typically measured in kilograms (kg). In this question, the mass of the body is given as 100 kg.

Acceleration:
Acceleration is the rate at which an object changes its velocity. It is a vector quantity and is typically measured in meters per second squared (m/s^2). In this question, the acceleration of the body is given as 5 m/s^2.

Force and Newton's Second Law

Force:
Force is defined as any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction. It is a vector quantity and is typically measured in Newtons (N).

Newton's Second Law:
Newton's second law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, it can be expressed as F = m * a, where F is the force, m is the mass, and a is the acceleration.

Calculating the Force

In this question, we are given the mass of the body as 100 kg and the acceleration as 5 m/s^2. We need to calculate the force applied to produce this acceleration.

Using Newton's second law, we can substitute the given values into the equation:

F = m * a
F = 100 kg * 5 m/s^2
F = 500 N

Therefore, the force applied on the body to produce an acceleration of 5 m/s^2 is 500 N.

Conclusion:
The correct answer is option C) 500 N.

If tension in the cable supporting a lift moving downwards is half the tension when it is moving upwards, the acceleration of the lift is
  • a)
    g/2
  • b)
    g/3
  • c)
    g/4
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Pritam Jain answered
When lift is at rest: T = mg
When lift is accelerating upward: TU = mg + ma
When lift is accelerating downward: TD = mg - ma
TU = 2TD
mg + ma = 2mg - 2ma
a = g/3

A person who weighs 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?
  • a)
    400 N
  • b)
    800 N
  • c)
    1000 N
  • d)
    1200 N
Correct answer is option 'D'. Can you explain this answer?

Amrita Chauhan answered
The person exerts a downward force on the scale, and the scale pushes up on the person with an equal (but opposite) force, FN. Thus, the scale reading is FN, the magnitude of the normal force.
FN – FW = ma ⇒ FN – mg = ma
⇒ FN = ma + mg = m (a + g) = (W/g) (a + g) = (800/10) (10 + 5)
FN = 1200 N

A couple is formed when:
  • a)
    Two unequal and unlike parallel force acting on a body
  • b)
    Two unequal and like parallel force acting on a body
  • c)
    Two equal and unlike parallel force acting on a body
  • d)
    Two equal and like parallel force acting on a body
Correct answer is option 'C'. Can you explain this answer?

Aditya Majumdar answered
Understanding Couples in Mechanics
A couple is a fundamental concept in mechanics, particularly in the study of forces and their effects on bodies. It consists of two equal and opposite forces that create a rotational effect without causing any linear motion.
Key Characteristics of a Couple:
- Two Equal Forces: A couple is formed by two forces that are equal in magnitude. This ensures that the forces balance each other out in terms of linear motion.
- Unlike Directions: The forces act in opposite directions. This opposition is crucial as it creates a torque or moment about a point.
- Parallel Forces: The forces in a couple are parallel to each other, meaning they do not intersect. This parallel nature is essential for ensuring that the rotational effect is produced without any net force acting on the body.
Why Option 'C' is Correct:
- Equal and Unlike Forces: Option 'C' states that a couple is formed by two equal and unlike parallel forces. This aligns perfectly with the definition and characteristics of a couple.
- Resulting Torque: The equal and opposite nature of the forces generates a torque, which tends to make the body rotate about an axis. The magnitude of the torque is calculated as the product of one of the forces and the perpendicular distance between the lines of action of the forces.
Conclusion:
Understanding the concept of couples is vital in mechanical engineering. It applies to various scenarios, from simple lever systems to complex machinery. Recognizing that a couple consists of two equal and unlike parallel forces is essential for analyzing rotational systems effectively.

A rubber ball is dropped from a height of 2 m. If there is not loss of velocity after rebounding the ball will rise to a height of
  • a)
    1 m
  • b)
    2 m
  • c)
    3 m
  • d)
    4 m
Correct answer is option 'B'. Can you explain this answer?

Kalyan Chakraborty answered
Conservation of energy:
P.E1+K.E1=P.E2+K.E2P.E1+K.E1=P.E2+K.E2
As there is no loss of velocity so
K.E=12mv2⇒K.E1=K.E2K.E=12mv2⇒K.E1=K.E2
P.E1=P.E1⇒h1=h2⇒h2=2m

A 50 - kg box rests on horizontal floor for which coefficient of friction is 0.3. If the box is subjected to a horizontal towing force of 400 N, what is its velocity after 5 sec from rest? (Take g = 10 m/s2) 
  • a)
    40 m/s
  • b)
    30 m/s
  • c)
    27.5 m/s
  • d)
    25 m/s
Correct answer is option 'D'. Can you explain this answer?

Asha Basu answered
Initially checking whether towing force can overcome the static friction force or not.
Friction force (f) = μN = μmg = 0.3 × 50 × 10 = 150 N
∴ Net force on box = 400 – 150 = 250 N
⇒ 250 = ma
Velocity after 5 second
V = u + at = 0 + 5 × 5 = 25 m/s

A car moving with uniform acceleration cover 450 m in a 5 second interval, and covers 700 m in the next 5 second interval. The acceleration of the car is
  • a)
    7 m/s2
  • b)
    50 m/s2
  • c)
    25 m/s2
  • d)
    10 m/s2
Correct answer is option 'D'. Can you explain this answer?

Vaibhav Khanna answered
Given :
Initial distance of the car (s)= 450 m .
Initial time taken (t)= 5 s .
Initial velocity of the car ( u ) = 450 m / 5 s ⇒ 90 m/s .
Final distance covered by the car = 700 m .
Final time taken by the car = 5 s .
Final velocity of the car ( v )= 700 m / 5 s ⇒ 140 m/s .
Time taken to change the velocity ( t ) = 5 s .
Acceleration is the rate of change of velocity per unit time .
at t = 5 sec, s = 450 m
at t = 10 sec
s = 450 + 700 = 1150
Equation (ii) – Equation (i), we get 
a = 10 m/s ^ 2
Hence, Correct answer is D
You can solve such questions and mock tests of Mechanical Engineering by going through the course:

On a ladder resting on a smooth ground and leaning against vertical wall, the force of friction will be:
  • a)
    Away from the wall at its upper end
  • b)
    Towards the wall at its upper end
  • c)
    Upwards at its upper end
  • d)
    Downwards at its upper end
Correct answer is option 'C'. Can you explain this answer?

Gayatri Dasgupta answered
Free body diagram of a ladder resting on a frictional surface is:
The force of friction will be upwards at its upper end and towards the wall at its lower end.
As the ground is smooth (but the wall does not), so fA = 0 and fB ≠ 0
So the force of friction will be upwards at its upper end.

Which of the following forces have zero value of resultant?
  • a)
    Non - concurrent forces
  • b)
    Non - coplanar forces
  • c)
    Coplanar forces
  • d)
    Equilibrium forces
Correct answer is option 'D'. Can you explain this answer?

Prateek Mukherjee answered
Equilibrium is the status of the body when it is subjected to a system of forces. If the resultant force is equal to zero it implies that the net effect of the system of forces is zero this represents the state of equilibrium.

The angular velocity (in radians /sec) of a body rotating at N rpm is:
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

Ameya Kaur answered
Rpm is just a measure of how many times a point is revolving per minute.
In a single revolution, a point rotates an angle = 2π
So, the total angle a point is rotating per minute = N x 2 π
The angular velocity is a measure of how fast it is rotating = Angle Rotated/Time Required = 2π N/60

The sum of kinetic and potential energy of a falling body _____.
  • a)
    Is constant at all points
  • b)
    Varies from point to point
  • c)
    Is maximum at starting and goes on increasing
  • d)
    Is maximum at starting and goes on decreasing
Correct answer is option 'A'. Can you explain this answer?

Anjali Sengupta answered
Kinetic energy  represents energy the mass possesses by virtue of its motion. Likewise, potential energy (PE=mgh) represents energy the mass possesses by virtue of its position.
E=KE+PE
E is the total energy of the mass: i.e., the sum of its kinetic and potential energies. It is clear that E is a conserved quantity: i.e., although the kinetic and potential energies of the mass vary as it falls, its total energy remains the same and one form of energy is being converted into other form of energy.

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