Q. 18

A uniform sphere of mass m and radius R is placed on a rough horizontal surface (Fig. 7.9). The sphere is struck horizontally at a height h from the floor. Match the following:

A. h = R/2 (i) Sphere rolls without slipping with a constant velocity and no loss of energy.

B. h = R (ii) Sphere spins clockwise, loses energy by friction.

C. h = 3R/2 (iii) Sphere spins anti-clockwise, loses energy by friction.

D. h = 7R/5 (iv) Sphere has only a translational motion, loses energy by friction.

Answer :

Applying conservation of angular momentum just before and after collision.

And as there is rolling without slipping

So, sphere will roll with slipping (no loss of energy) when

So, d-(i)

Torque due to applied force about centre of mass

If h=R then

Therefore, sphere will only have translational motion and loose energy by friction.

So, b-(iv)

If h>R, then torque is positive. Hence sphere will spin clockwise.

So, c-(ii)

If h<R, then torque is negative. Hence sphere will spin anticlockwise.

So, a-(iii)

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