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A solid sphere and a hollow sphere of eq...

A solid sphere and a hollow sphere of equal mass and radius are placed over a rough horizontal surface after rotating it about its mass centre with same angular velocity `omega_(0)`. One the pure rolling starts let `v_(1)` and `v_(2)` be the linear speeds of their centers of mass. Then

A

`v_(1) =v_(2)`

B

`v_(1) gt v_(2)`

C

`v_(1) lt v_(2)`

D

data insufficent

Text Solution

Verified by Experts

The correct Answer is:
C
From conservation of angular momentum about point of contact.
`Iomega_(0) = I_(omega) + mRv` or `Iomega_(OR) = Iv/R + mRv`
or `v=(Ia_(0))/(I/R + mR)` or `v=omega_(0)/(1/R + (mR)/I)`

Now `I_("solid sphere") lt I_("solid") therefore v_("solid") lt v_(hollow") therefore v_(1) lt v_(2)`
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