A solid sphere of mass `m` and radius `R` is gently placed on a conveyer belt moving with constant velocity `v_(0)`. If coefficient of friction between belt and sphere is `2//7` the distance traveled by the centre of the sphere before it starts pure rolling is

Options

A. `v_(0)^(2)/(7g)`
B. `(2v_(0)^(2))/(49g)`
C. `(2v_(0)^(2))/(5g)`
D. `(2v_(0)^(2))/(7g)`

Answer

A

Explanation

`N mu =ma rArr a = gmu rArr NmuR = 2/3 mR^(2) alpha rArr (5g mu)/(2R) v=gmut, omega =(5 gmu)/(2R)t`
Pure rolling starts when `v+R omega =v_(0)`
`rArr gmut + 5/2 g mut =v_(0) rArr t=(2v_(0))/(7g mu)`

`s=1/2 at^(2) =1/2 gmu (4v_(0)^(2))/(49 g^(2)mu^(2)) = (2v_(0)^(2))/(49 gmu) rArr s =(2v_(0)^(2))/(49g(2//7)) v_(0)^(2)/(7g)`