Circular Motion MSQ


10 Questions MCQ Test Basic Physics for IIT JAM | Circular Motion MSQ


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Attempt Circular Motion MSQ | 10 questions in 45 minutes | Mock test for Physics preparation | Free important questions MCQ to study Basic Physics for IIT JAM for Physics Exam | Download free PDF with solutions
*Multiple options can be correct
QUESTION: 1

One end of a light string of length L is connected to a ball and the other end is connected to a fixed point O. The ball is released from rest at t = 0 with string horizontal and just taut. The ball then moves in vertical circular path as shown. The time taken by ball to go from position A to B is t1 and from B to lowest position C is t2. Let the velocity of ball at B is  and at C is   respectively. If   then, which of the following is true.

Solution:

Tangential acceleration is at = g cos θ which decrease with time.

Hence the plot of at versus time may be as shown in graph.

Area under graph in time interval t1 = vB – 0 = vB

Area under graph in the time interval t2 = vC – vB = vB

Hence the under graph in time t1 and t2 is same.

∴  t1 < t2

∴ t1 < t2

The correct answers are: 

*Multiple options can be correct
QUESTION: 2

A machine, in an amusement park, consists of a cage at the end of one arm, hinged at O. The cage revolves along a vertical circle of radius r (ABCDEFGH) about its hinge O, at constant linear speed   The cage is so attached that the man of weight ‘w’ standing on a weighing machine, inside the cage, is always vertical. Then which of the following is/are correct.

Solution:

Let N be the normal reaction (Reading of the weighing machine)

Put v ∴  NA – mg = mg
⇒  NA = 2mg = 2W

hence  NA > NE by 2W
Now at GNG = mg = W = Nc

The correct answers are: the weight reading at A is greater than the weight reading at E by 2 w, the weight reading at G = w, the ratio of the weight reading at E to that at A = 0, the ratio of the weight reading at A to that at C = 2

QUESTION: 3

A particle is moving in a circular path. The acceleration and momentum vectors at an instant of time are  Then which of the following statement is incorrect

Solution:

*Multiple options can be correct
QUESTION: 4

A car driver going at some speed suddenly finds a wide wall at a distance r. To avoid hitting the wall he should.

Solution:

When he applies brakes

if µ is the friction coefficient then a = µg


when he takes turn 

 

Then we can see r < s1 hence driver can hit the wall when he take turn due to insufficient radius of curvature.

The correct answer is: apply the brakes

*Multiple options can be correct
QUESTION: 5

Two particles A and B separated by a distance 2R are moving counter clockwise along the same circular path of radius R each with uniform speed v. At time t = 0. A is given a tangential acceleration of magnitude 

Solution:

As when they collide 


Now angle covered by 

Put t ∴ angle covered by 

The correct answers are: the time lapse for the two bodies to collide is  the angle covered of A is 11π/6

*Multiple options can be correct
QUESTION: 6

A smooth rod PQ rotates in a horizontal plane about its mid point M which is h = 0.1 m vertically below a fixed point A at a constant angular velocity 14 rad/s. A light elastic string of natural length 0.1 m force constant 1.47 N/cm has one end fixed at A and its other end attached to a ring of mass m = 0.3 kg which is free to slide along the rod. When the ring is stationary relative to rod, then which of following is correct.

Solution:

but R = Kx
(K = 1.47 × 102 N/m)
Also  r = 0.1 tan θ
put Trm  and ω in equation (2)
We have cos θ = 3/5 and T = 9.8 N
The correct answers are: Tension in spring is 9.8 N, Inclination of string with vertical is cos–1(3/5)

*Multiple options can be correct
QUESTION: 7

On a circular table, A and B are moving on the circumference. Man A runs behind man B to catch him A runs with constant angular speed  ω1 with respect to table and B runs at constant tangential speed v2 with respect to ground. If it is found that the table rotates 30° in the opposite direction in every one second and the initial angular separation between A and B is 30°, then A catches B after : (Radius of table is 3 m).

Solution:




The correct answers are: 0.5 sec, if    A can not catch B within 0.5 sec  

*Multiple options can be correct
QUESTION: 8

A small sphere of mass m suspended by a thread is first taken aside so that the thread forms the right angle with the vertical and then released, then :

Solution:

By putting the value of VB

TB = 3mg cosθ

When total acceleration vector directed horizontally

The correct answers are: total acceleration of sphere as a function of  thread tension as a function of θ is T = 3mg cos θ between the thread and the vertical at the moment when the total acceleration vector of the sphere is directed horizontal is 

*Multiple options can be correct
QUESTION: 9

A section of fixed smooth circular track of radius 20 m, in vertical plane is shown in the figure. A block is released from position A and leaves the track at B :

Solution:

By energy conservation between A and B

Now, radius of curvature 

The correct answers are: velocity at point B is   Radius of curvature of trajectory when leaves point B is R/2

*Multiple options can be correct
QUESTION: 10

A particle is describing circular motion in a horizontal plane in contact with the smooth inside surface of a fixed right circular cone with its axis vertical and vertex down. The height of the plane of motion above the vertex is h and the semi-vertical angle of the cone is α. The period of revolution of the particle :

Solution:

Thus when h increases T also increases.
The correct answers are: increases as h increases, increases as α  increases

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