Q18 of 28 Page 53

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.



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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