Revision Quiz | Rotational Motion for JEE & BITSAT Exams

Question 1

A uniform metallic spherical shell is suspended by threads. It has two holes A and B at top and bottom respectively, as shown in figure. Then-

Question 2

Three masses 2 kg, 3 kg and 4 kg are lying at the corners of an equilateral triangle of side ℓ. The (X) coordinate of center of mass is –

Question 3

Two identical blocks having mass M each are smoothly conjugated and placed on a smooth horizontal floor as shown in the figure. On the left of block A, there is a wall. A small block of mass m is released from the position shown in the figure. The velocity of block B is maximum,

Question 4

Find out the center of mass of an isosceles triangle of base length 10 m and altitude 15 m. Assume that the mass of the triangle is uniformly distributed over its area.

Question 5

A cylinder rolls without slipping over a horizontal plane. The radius of the cylinder is r. Find the curvature radii of trajectories traced by the points A and B. See figure.

Question 6

Three identical cars A, B and C are moving at the same speed on three bridges. The car A goes on plane bridge. B on a bridge convex upwards and car C on a bridge concave upwards. Let F_A, F_B and F_C be the normal forces exerted by the cars on the bridges when they are at the middle of bridge -

Question 7

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross-section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will-

Question 8

A wheel of radius r = 10 cm and moment of inertia I= 0.02 kg m² about its axis is fixed at the top of an inclined plane of inclination 30^o as shown in the figure. A string is wrapped around the wheel and its free end supports a block of mass m of 2 Kg which can slide on the plane. Initially, the wheel is rotating at a speed of 20 rad/sec in a direction such that the block slides up the plane. How far will the block move before stopping?

Question 9

A bullet of mass m moving with velocity u just grazes the top of a solid cylinder of mass M and radius R resting on a rough horizontal surface as shown in the figure. Assuming that the cylinder rolls without slipping. Find the final velocity of the bullet and angular velocity of the cylinder.

Question 10

Each of the blocks shown in the figure has mass 1 kg. The rear block moves with a speed of 2 m/s towards the front block kept at rest. The spring attached to the front block is light and has a spring constant 50 N/m. Find the maximum compression of the spring.

Question 11

As shown in figure A, B and C are identical balls B and C are at rest and, the ball A moving with velocity v collides elastically with ball B, then after collision –

Question 12

2n identical cubical blocks are kept in a straight line on a horizontal smooth surface. The distance between the consecutive blocks in same. The blocks 1, 3, 5,.....(2n – 1) are given velocity v to the right whereas blocks 2, 4, 6,......2n are given velocity to the left. All collisions between blocks are perfect elastic. The total number of collisions that will take place is –

Question 13

A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness 4t. The relation between the moments of inertia I_A and I_B is-

Question 14

A scientist is given two heavy spheres made of the same metal, which have the same diameter and the weight, and is asked to distinguish the sphere, without damaging them in any way. Though the sphere look like identical, one of them is actually a hollow spherical shell, while the other is a set of concentric shells mounted on four thin rods of the same metal as shown below.

To make this distinction, the scientist must perform an experiment where each sphere is

Question 15

The moment of inertia of a rod about an axis through its centre and perpendicular to it is

ML²(where, M is the mass and L the length of the rod). The rod is bent in the middle to that the two halves make an angle of 60⁰. The moment of inertia of the bent rod about the same asix would be