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

Options

A. `v_(1)=v_(2)`
B. `v_(1)ltv_(2)`
C. `v_(1)gtv_(2)`
D. data is insufficient

Answer

C

Explanation

Form conservation of angular momentum about point of contact.

`Iomega_(0)=Iomega+mRomega`
`Iomega_(0)=I(v^(2))/R+mRv`
`v=(Iomega_(0))/(I/R+mR)impliesv=(omega_(0))/(1/R+(mR)/1)`
Now `I_("solid sphere") lt I_("hollow") `
`v_("solid")lt v_("hollow")`
`v_(1)ltv_(2)`