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All questions of Motion in a Plane for Class 11 Exam

If 14511_image012 what is the angle between 14511_image013 and 14511_image014
  • a)
    900
  • b)
    300
  • c)
    600
  • d)
    450
Correct answer is option 'D'. Can you explain this answer?

Gaurav Kumar answered
We know that for two vectors P and Q
P.Q = |P||Q| cos a
And PxQ = |P||Q| sin a
Where a is angle between them
When P.Q = PxQ
We get sin a = cos a
Thus a = 450
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A car travelling at 36km/h-1 due North turns West in 5 seconds and maintains the same speed. What is the acceleration of the car?
  • a)
    2√2ms-2  South West
  • b)
    √2ms-2  South West
  • c)
    2ms-2 North West
  • d)
    4ms-2 North West
Correct answer is option 'A'. Can you explain this answer?

Rahul Bansal answered
Initial velocity of car = 36 km/hr due north 
Final velocity of car = 36 km/hr due west

magnitude of change in velocity = root[(36)^2 + (36)^2] = 36 x √2
(since velocity is a vector, so direction has to be taken into account)

Acceleration =  Change in velocity/time = [36√2 x 5/18]/5 m/s^2 = 2√2 m/s^2 = 2.828 m/s^2

A boat sails across a river with a velocity of 10 km/hr. If resultant boat velocity is 14 km/hr, then what is the velocity of river water? 
  • a)
     17.20 km/hr
  • b)
     10 km/hr
  • c)
     9.79 km/hr 
  • d)
     4.88 km/hr
Correct answer is option 'C'. Can you explain this answer?

Om Desai answered
We can use the Pythagorean theorem to solve this problem since the boat's velocity, river's velocity, and resultant velocity form a right triangle.

Let the boat's velocity be represented by A (10 km/hr), the river's velocity be represented by B, and the resultant velocity be represented by C (14 km/hr).

According to the Pythagorean theorem, A^2 + B^2 = C^2.

Now, we can plug in the given values and solve for B:

(10)^2 + B^2 = (14)^2
100 + B^2 = 196

Subtract 100 from both sides:

B^2 = 96

Now, take the square root of both sides:

B = sqrt(96) ≈ 9.79 km/hr

 A particle moves in x-y plane starting from the origin in a direction making 30° angle with x-axis. Distance covered by it is 5 m. what is the position vector of the particle.
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

Ankita Menon answered
Initial velocity = u = 20 m/s 
Final velocity = v = 0              [ at maximum height , v = 0 ]
Acceleration due to gravity(g)  in this case , is taken as negative.
This is because , when the direction of motion of object is opposite to "g" , then value of g is taken as -ve
hence ,
g = -9.8 m/s²
Let's use the formula :-
[h = height ]
v² -u² = 2gh
0² - 20² = 2*-9.8*h
-400 = -19.6h
h = -400/-19.6
  = 20.408 m [ approximately ]

 How many directions are possible for the same horizontal range?
  • a)
    4
  • b)
    3
  • c)
    2
  • d)
    1
Correct answer is option 'C'. Can you explain this answer?

Mira Joshi answered
We know that the horizontal range for any projectile motion let say R = 2u2.sin 2a /g
Where u is initial speed, and a is the angle at which the particle is thrown, which is responsible for direction. So in between the possible range of a that is 0 - 90, there are maximum two equal values of sin 2a, thus the maximum number of directions for the same or equal range are 2.

A particle has an initial velocity 3 iˆ +4 jˆ and an acceleration 0.4 iˆ + 0.3 jˆ .Its speed after 10 s is
  • a)
    7 units
  • b)
    8.5 units
  • c)
    7√2 units
  • d)
    10 units
Correct answer is 'B'. Can you explain this answer?

Mira Sharma answered
Answer is C) 7 x (2)^1/2

Solution:
The initial velocity is given by

u = v - at

Where, v = Final Velocity, t = time taken, and a = acceleration

u = 3 i + 4 j

a = 0.4 i + 0.3 j

t = 10 s

Using initial velocity formula

3 i + 4 j = v - (0.4 i + 0.3 j) 10

v = 7 ( i + j)

Velocity is the vector quantity which is defined by both magnitude and direction but speed is scalar quantity which is defined by only magnitude.

The magnitude of v = (7^2+7^2)^1/2 = 7 x (2)^1/2

 If an object is dropped through the window of a fast running train. Then
  • a)
    the object moves straight horizontally.
  • b)
    to a man standing near the track, path of the object will be a part of parabola.
  • c)
    the object falls down vertically.
  • d)
    the object will follow an elliptical path
Correct answer is option 'B'. Can you explain this answer?

Suresh Reddy answered
When an object is still held it is the part of a system in which the train is moving, once it is left it still has the same velocity as the train for a person from ground. Thus as the velocity is horizontal and acceleration is vertical, it would follow a parabolic trajectory.

Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella?
  • a)
    cos-1 1/3
  • b)
    sin-1 1/3
  • c)
    tan-1 2/3
  • d)
    tan-1 1/3
Correct answer is option 'D'. Can you explain this answer?

Krishna Iyer answered
When the man rides, he should put an umbrella in the opposite direction to which the drops are falling with respect to him.
Hence wrt man, the speed of rain drop is
at an angle of tan-1 ⅓
Hence he would put umbrella to the direction of tan-1 ⅓

A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top
  • a)
    1 s       
  • b)
    2 s
  • c)
    4 s       
  • d)
    16 s
Correct answer is option 'B'. Can you explain this answer?

Naina Sharma answered
A body start from rest so, u = 0 
Let total distance covered = s
Let a body moves with accerlation = a 
► s = 1/2 × a× t2
► s = 1/2× a × 42
► s = 8a
The one-fourth of total distance, s'  = 8a/4
= 2a
► s' = 1/2 × a × t2
► 2a / a = 1/2 × t2
► 4 = t2
► t = 2 s

A body is thrown with a velocity of 10m/s at an angle of 60 degrees with the horizontal. Its velocity at the highest point is: 
  • a)
    5 m/s
  • b)
    8.7 m/s
  • c)
    10 mis
  • d)
    0
Correct answer is option 'A'. Can you explain this answer?

Mira Joshi answered
At the highest point, its vertical velocity will become zero. Hence the only left velocity is horizontal which remains unchanged and is equal to 10 cos 60 = 5m/s

A battle ship simultaneously fires two shells at enemy ships. Both are fired with the same speed but with different directions as shown. If the shells follow the parabolic trajectories shown, which ship gets hit first?
  • a)
    they get hit at the same time.
  • b)
    ship μ2
  • c)
    need more information about the trajectories.
  • d)
    ship μ1
Correct answer is 'B'. Can you explain this answer?

Krishna Iyer answered
Ship 2 gets hit first. The time of flight only depends on the y-component of motion, not the x-component.  The higher you throw something up in the air, the more time it spends in the air.  It can also be shown from equation-
y=v0y t – ½ g t2=0  
    v0y for projectile μ1 is greater than for μ2.

Vectors can be added by
  • a)
    adding the magnitudes of the vectors
  • b)
    adding the angles of the vectors
  • c)
    translating the two vectors
  • d)
    parallelogram law of addition
Correct answer is option 'D'. Can you explain this answer?

Puja Kaur answered
Explanation:Parallelogram law of vector addition is,If two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a diagonal passing through the point of contact of two vectors.

 The vector which when added to the resultant of  12764_0_4_ and  12764_shritiiii20gives unit vector along x direction.
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?

Naveen Choudhary answered
Time taken by first drop to cover 5 cm, u = 0
⇒ h = 1/2 gt2
⇒ 5 = 1/2 x 10 x t2
⇒ t = 1 sec
Hence interval is 0.5 sec for each drop.
Now distance fallen by second drop in 0.5 sec
⇒ h1 = 1/2 gt2
         = 1/2 x 10 x (0.5)2
         = 5 x 0.25
         = 1.25 m
Height above the ground ( of 2nd drop) = 5 - 1.25
= 3.75 m
 

When a projectile is thrown up at an angle θ to the ground, the time taken by it to rise and to fall are related as
  • a)
    time of rise can be less than or equal to time of fall
  • b)
    they are equal
  • c)
    time of rise < time of fall
  • d)
    time of rise > time of fall
Correct answer is option 'B'. Can you explain this answer?

Gaurav Kumar answered
The time of fall or rise for a projectile depends upon its vertical component of initial velocity and the vertical acceleration. As the acceleration does not change and the motion of path is identical for the rise phase and the fall phase, we can easily deduce that time taken is also the same.

At the point of maximum height, the acceleration is:
  • a)
    minimum
  • b)
    g
  • c)
    maximum
  • d)
    zero
Correct answer is option 'B'. Can you explain this answer?

Suresh Iyer answered
At a point of maximum height, the derivative of displacement i.e. velocity is zero but as the gravitational acceleration is equal at all near points to the surface of earth, acceleration at maximum height is still equal to g.

Uniform circular motion is called continuously accelerated motion mainly because its :
  • a)
    direction of motion changes
  • b)
    speed remains the same
  • c)
    velocity remains the same
  • d)
    direction of motion does not change
Correct answer is option 'A'. Can you explain this answer?

Krishna Iyer answered
An accelerating body is an object that is changing its velocity. And since velocity is a vector that has both magnitude and direction, a change in either the magnitude or the direction constitutes a change in the velocity.
Hence a uniform circular motion is a accelerated motion because direction of motion keeps on changing

Which of the following is not a scalar quantity?
  • a)
    Temperature
  • b)
    Coefficient of friction
  • c)
    Charge
  • d)
    Impulse
Correct answer is option 'D'. Can you explain this answer?

Vivek Patel answered
Impulse (I)

Since force is a vector quantity and impulse is the product of the sudden force applied and the time interval to bring equivalent the system. So Impulse also a vector quantity which have same direction to the force applied.

Which of the following statements not true?
  • a)
    The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point
  • b)
    The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector
  • c)
    The net acceleration of a particle in uniform circular motion is always along the radius of the circle towards the centre
  • d)
    The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre
Correct answer is option 'D'. Can you explain this answer?

Jyoti Shah answered
Understanding Circular Motion and Acceleration
In circular motion, it's crucial to differentiate between uniform and non-uniform circular motion. The statements provided touch on these concepts.
Analysis of Each Statement
- Statement A: The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
This statement is true. In circular motion, the velocity is tangential to the circle.
- Statement B: The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.
This statement is also true. Over one full cycle, the direction of the acceleration changes but the average vector sums to zero.
- Statement C: The net acceleration of a particle in uniform circular motion is always along the radius of the circle towards the center.
This statement is true. In uniform circular motion, the acceleration (centripetal) is directed inward toward the center.
- Statement D: The net acceleration of a particle in circular motion is always along the radius of the circle towards the center.
This statement is false. While centripetal acceleration is always directed towards the center in uniform circular motion, in non-uniform circular motion, tangential acceleration exists, which is not directed towards the center. Therefore, the net acceleration can have components both radial and tangential.
Conclusion
The correct answer is option 'D' as it incorrectly suggests that the net acceleration is always directed towards the center, ignoring the possibility of tangential acceleration in non-uniform circular motion.

A particle has an initial velocity 3 iˆ +4 jˆ and an acceleration 0.4 iˆ + 0.3 jˆ .Its speed after 10 s is
  • a)
    7 units
  • b)
    8.5 units
  • c)
    7√2 units
  • d)
    10 units
Correct answer is option 'B'. Can you explain this answer?

Nandini Patel answered
Answer is C) 7 x (2)^1/2

Solution:
The initial velocity is given by

u = v - at

Where, v = Final Velocity, t = time taken, and a = acceleration

u = 3 i + 4 j

a = 0.4 i + 0.3 j

t = 10 s

Using initial velocity formula

3 i + 4 j = v - (0.4 i + 0.3 j) 10

v = 7 ( i + j)

Velocity is the vector quantity which is defined by both magnitude and direction but speed is scalar quantity which is defined by only magnitude.

The magnitude of v = (7^2+7^2)^1/2 = 7 x (2)^1/2

The driver of a car moving towards a rocket launching pad with a speed of 6 ms−1 observed that the rocket is moving with a speed of 10 ms−1 the upward speed of the rocket as seen by the stationary observer is
  • a)
    4 ms−1
  • b)
    6 ms−1
  • c)
    11 ms−1
  • d)
    8 ms−1
Correct answer is option 'D'. Can you explain this answer?

Jithin Nair answered
-1 suddenly sees a rocket launching vertically upwards with a velocity of 80ms-1. What is the relative velocity of the car with respect to the rocket?

The relative velocity of the car with respect to the rocket can be found by adding the velocity of the car and the velocity of the rocket.

Relative velocity = velocity of car + velocity of rocket
Relative velocity = 6 ms-1 + 80 ms-1
Relative velocity = 86 ms-1

Therefore, the relative velocity of the car with respect to the rocket is 86 ms-1.

Which one of the following is not an example of projectile?
  • a)
    A  bullet fired from a gun.
  • b)
    A kicked football.
  • c)
    Taking off of an aircraft.
  • d)
    A javelin thrown by an athlete.
Correct answer is option 'C'. Can you explain this answer?

Top Rankers answered
A projectile is any object thrown into space upon which the only acting force is gravity. A bullet fired from a gun, a kicked football, and a javelin thrown by an athlete are examples of projectiles once they are in motion and only gravity acts on them. Taking off of an aircraft is not a projectile because it involves continuous external force from the engines.

A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity u. The ratio of their velocities when they reach the earth’s surface will be
  • a)
  • b)
    1 : 2
  • c)
    1 : 1
  • d)
Correct answer is option 'C'. Can you explain this answer?

Ambition Institute answered
Particle 1 (Thrown Vertically Downward):
Initial velocity (u) is downward.
Final velocity is affected by gravity. Using the equation of motion:
Particle 2 (Thrown Horizontally):
Horizontal velocity remains constant (u).
Vertical velocity due to free fall can be calculated as:
The resultant velocity (v2) at the Earth's surface is given by combining the horizontal and vertical velocities using the Pythagorean theorem:
Velocity Ratio:
The magnitude of both velocities is the same:

Thus, the ratio of their velocities is: 1 : 1

We can define the difference of two vectors A and B as the
  • a)
    sum of two vectors A and B' such that B' is equal to B multiplied by 0
  • b)
    sum of two vectors A and B' such that B' is equal to B multiplied by -1
  • c)
    sum of two vectors A and B' such that B' is equal to B multiplied by -2
  • d)
    sum of two vectors A and B' such that B' is equal to B multiplied by 1
Correct answer is option 'B'. Can you explain this answer?

Surbhi Mishra answered
Explanation:
Vector subtraction is defined in the following way.
  • The difference of two vectors, A - B , is a vector C that is, C = A - B
  • The addition of two vector such that C = A + (-B). B has been taken in opposite direction.
Thus vector subtraction can be represented as a vector addition.

In a harbor, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbor flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?
  • a)
    approximately north
  • b)
    approximately north-east
  • c)
    approximately east
  • d)
    approximately south
Correct answer is option 'C'. Can you explain this answer?

Ankita Patel answered
Explanation:The flag is fluttering in the north-east direction. It shows that the wind is blowing toward the north-east direction. When the ship begins sailing toward the north, the flag will move along the direction of the relative velocity (vwb) of the wind with respect to the boat.
Hence, the flag will flutter approximately due east.

In circular motion:
  • a)
    Radial acceleration is non-zero
  • b)
    Radial velocity is zero
  • c)
    Body is in equilibrium
  • d)
    All of the above
Correct answer is option 'D'. Can you explain this answer?

Stuti Joshi answered
Circular motion involves the motion of an object in a circular path. The object moves around the center of the circle with a constant speed. In circular motion, the object experiences various types of acceleration and velocity. Let’s discuss the given options to understand circular motion in detail.

Radial acceleration is non-zero:
Radial acceleration is the acceleration of an object towards the center of the circle. In circular motion, the direction of velocity changes continuously, and hence the object experiences a change in direction. This change in direction leads to the acceleration of the object towards the center of the circle, known as radial acceleration. Therefore, option ‘a’ is correct.

Radial velocity is zero:
Radial velocity is the velocity of an object in the radial direction, i.e., towards the center of the circle. In circular motion, the object moves in a circular path without any radial motion, i.e., the object moves perpendicular to the radius of the circle. Hence, radial velocity is zero in circular motion. Therefore, option ‘b’ is incorrect.

Body is in equilibrium:
Equilibrium is a state where the object is at rest or moves with a constant velocity. In circular motion, the object moves with a constant speed, but the direction of the velocity changes continuously. Therefore, the object is not at rest, but it is also not moving with a constant velocity. Hence, the body is not in equilibrium in circular motion. Therefore, option ‘c’ is incorrect.

All of the above:
From the above discussion, we can conclude that radial acceleration is non-zero, radial velocity is zero, and the body is not in equilibrium in circular motion. Therefore, option ‘d’ is the correct answer.

Conclusion:
Circular motion involves the motion of an object in a circular path. The object experiences various types of acceleration and velocity in circular motion. In circular motion, radial acceleration is non-zero, radial velocity is zero, and the body is not in equilibrium.

In circular motion, the
  • a)
    Direction of motion is fixed
  • b)
    Direction of motion changes continuously
  • c)
    Acceleration is zero
  • d)
    Velocity is constant
Correct answer is option 'B'. Can you explain this answer?

Hansa Sharma answered
When an object moves along a circular path, it is called circular motion. During such a motion, the direction of motion at any point is given by the tangent at that point which changes continuously.

Rain is falling vertically with a speed of 30 m s−1. A woman rides a bicycle with a speed of 10 m s−1 in the north to south direction. What is the direction in which she should hold her umbrella?
  • a)
    about 18∘ with the vertical, towards the south
  • b)
    about 28∘ with the vertical, towards the south
  • c)
    about 28∘ with the vertical, towards the north
  • d)
    about 18∘ with the vertical, towards the north
Correct answer is option 'A'. Can you explain this answer?

Jyoti Kapoor answered

In order to protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to the woman.

v = vr + (-vc)
= 30 + (-10) = 20 m/s
tan θ = vc / vr = 10 / 30
θ = tan^-1 (1 / 3)
= tan^-1 (0.333) ≈ 18 degree

Hence, the woman must hold the umbrella toward the south, at an angle of nearly 18 degree with the vertical.

The _______ circular motion describes as the motion of an object in a circular path with a _______ speed. Fill in the blank.
  • a)
    Non-uniform, constant
  • b)
    Uniform, constant
  • c)
    Non-uniform, varying
  • d)
    Uniform, Varying
Correct answer is option 'B,C'. Can you explain this answer?

Simran Chauhan answered
Understanding Circular Motion
Circular motion can be categorized into two types based on the speed of the object moving along the circular path: uniform and non-uniform circular motion.
Uniform Circular Motion
- Definition: This occurs when an object moves in a circular path at a constant speed.
- Key Characteristics:
- The magnitude of the velocity remains constant.
- The direction of the velocity changes continuously, which implies that the object is accelerating towards the center of the circle (centripetal acceleration).
- An example is a satellite orbiting Earth at a fixed speed.
Non-Uniform Circular Motion
- Definition: This involves an object moving in a circular path but with varying speed.
- Key Characteristics:
- The speed of the object changes; it can either accelerate or decelerate.
- The object experiences both centripetal acceleration (due to changing direction) and tangential acceleration (due to changing speed).
- An example includes a car taking a curve while speeding up or slowing down.
Correct Answer Explanation
The question allows for two correct options:
- Option B: Uniform, Constant
- This describes the scenario where an object maintains a constant speed in a circular path.
- Option C: Non-uniform, Varying
- This describes the scenario where the speed of the object changes while still moving in a circular path.
Both options reflect different characteristics of circular motion, making them valid answers depending on the context. Understanding these types is crucial for analyzing motion in physics.

A body is projected with velocity 20√3 m/s with an angle of projection 60° with horizontal. Calculate velocity on that point where body makes an angle 30° with the horizontal.
  • a)
    20 m/s
  • b)
    20 /√3 m/s 
  • c)
    10 /√3 m/s 
  • d)
    10 m/s
Correct answer is option 'A'. Can you explain this answer?

Mohit Rajpoot answered
The velocity of the body at any point during its motion is composed of:
  1. Horizontal Component (vx): This remains constant throughout the motion because there’s no horizontal acceleration.

    Using cos ⁡60∘ = 1/2
  2. Vertical Component (vy): This changes with time due to the acceleration due to gravity (g = 9.8 m/s2). At the point where the angle with the horizontal is 30∘, the relation between the components of velocity is:
     ​ ​
    Using tan ⁡ 
     ​ ​
    Solve for vy​ :
  3. Magnitude of the Velocity (v): The total velocity is the vector sum of vx and vy​ :

    Substitute

Final Answer:
The speed of the body at the point where it makes an angle of 30∘ with the horizontal is: 20 m/s

Which of the following quantities is dependent of the choice of orientation of the coordinate axes?
  • a)
  • b)
    Ax + By
  • c)
  • d)
    Angle between
Correct answer is option 'B'. Can you explain this answer?

Dev Patel answered
A vector, its magnitude and the angle between two vectors do not depend on the choice of the orientation of the coordinate axes. So angle between are independent of the orientation of the coordinate axes. But the quantity Ax + By depends upon the magnitude of the components along x and y axes, so it will change with change in coordinate axes.

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