Q. Figure-5.102 shows a smooth inclined plane fixed in a car accelerating on a horizontal road. The angle of incline is related to the acceleration of the car as . If the sphere is set in pure rolling on the incline :

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A

It will continue pure rolling

B

It will slip down the plane

C

Its linear velocity will increase

D

Its linear velocity will decrease

Solution:

It will continue rolling because the inclined plane and sphere are initially at rest with respect to the car as pseudo force on sphere is balanced by .

Questions from System of Particles and Rotational Motion

1. Four point masses, each of value , are placed at the corners of a square of side . The moment of inertia of this system about an axis through and parallel to is

2. A solid cylinder rolls down an inclined plane of height 3 m and reaches the bottom of plane with angular velocity, of 2 . The radius of cylinder must be
(Take g = 10 )

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3. The radius of gyration of a uniform rod of length about an axis passing through its centre of mass is

4. A particle performing uniform circular motion has angular momentum . If its angular frequency is halved and its kinetic energy is doubled, then the new angular momentum is

5. A circular disc of radius is made from an iron plate of thickness , and another disc of radius is made from an iron plate of thickness . Then the relation between the moment of inertia and is

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