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.
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Options

A. `6 v_0//7` in forward direction
B. `6 v_0//7` in backward direction
C. `7 v_0//6` in forward direction
D. `7 v_0//6` in backward direction

Answer

A

Explanation

(a) Angular momentum can be conserved about lowest point
`mv_0 r + (2)/(5) mr^2 (v_0)/(2 r) = mv' r + (2)/(5) mr^2 (v')/( r)`
`(10 mv_0 r + 2mv_0 r)/(10) = (7 mv' r)/(5)`
`v' = (6 v_0)/(7)`.