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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