A hollow sphere of radius 2m 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
23
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B
43
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C
1
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D
32
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Solution
The correct option is B43
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=2m, v0ω0=2×23=43