Revision Quiz | Rotational Motion II for JEE & BITSAT Exams

Question 1

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc of reach its other end. During the journey of the insect, the angular speed of the disc

Question 2

A hoop of radius r and mass m rotating with an angular velocity

is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop when it ceases to slip?

Question 3

Let

be the force acting on a particle having position vector

and

be the torque of this force about the origin. Then

Question 4

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is: (Here, g is the acceleration due to gravity.)

Question 5

A small ball of mass m starts at a point A with speed

and moves along a frictionless track AB as shown. The track BC has coefficient of friction µ. The ball comes to stop at C after travelling a distance L which is :

Question 6

An annular ring with inner and outer radii R₁ and R₂ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F₁/F₂ is

Question 7

A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to:

Question 8

Figure shows a smooth inclined plane fixed in a car accelerating on a horizontal road. The angle of inclination θ is related to the acceleration a of the car as a=g tan θ. If the sphere is set in pure rolling on the inclined:

Question 9

A wheel of radius r rolls(rolling without slipping) on a level road as shown in the figure .Find out velocity of point A and B.

Question 10

For which of the following body, its translational and rotational kinetic energies will be equal when it is rolling down an inclined plane?

Question 11

From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is :

Question 12

For the given uniform square lamina ABCD, whose center is O,

Question 13

Seven identical circular planar disks, each of mass M and radius R, are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

Question 14

A thin uniform rod of length

and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its centre of mass rises to a maximum height of

Question 15

If system is at rest initially. Mass of A nd B is 5 kg and 10 kg, respectively. Radius of disk A is 20 cm. Find the height descended by the block B when A acquires a speed of 3 m/s. Assume there is no slipping. Take g =10 m/s²