1
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Question

# A hollow sphere of radius 2 m is projected horizontally along a rough surface with velocity v0 and angular velocity ω0. Find out their ratio so that the sphere stops moving after some time.

A
32
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B
43
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C
1
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D
23
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Solution

## The correct option is B 43 The hollow sphere is moving rightward. Hence, to oppose the rotational motion of the sphere, friction will act leftward at the contact point. Hence, about point P , τp=0 Therefore, applying conservation of angular momentum about point (P), →Li=→Lf When the sphere stops moving finally, both velocity and angular velocity become zero. ⇒Icom×ω0−mv0R=0+0 ⇒23mR2×ω0−mv0R=0 ⇒v0ω0=2R3 Now putting R=2 m, v0ω0=2×23=43

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