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A sphere of mass M and radius r shown in...

A sphere of mass `M` and radius `r` shown in figure slips on a rough horizontal plane. At some instant it has translational velocity `V_(0)` and rotational velocity about the centre `(v_(0))/(2r)`. Find the translational velocity after the sphere starts pure rolling.
.

A

`(5v_(0))/(7)`

B

`(6v_(0))/(7)`

C

`(3v_(0))/(4)`

D

`(3v_(0))/(5)`

Text Solution

Verified by Experts


By the conservation of angular momentum about `A`
`mv_(0)R+(2)/(5)mR^(2)(v_(0))/(2R)=mv_(c.m.)R+(2)/(5)mR^(2)((v_(c.m.))/(R ))`
`v_(c.m.)=(6v_(0))/(7)`
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