A solid sphere rests on a horizontal surface. A horizontal impulse is applied at height `h` from centre. The sphere starts rolling just after the application of impulse. The ratio `h//r` will be

Options

A. `11/2`
B. `2/5`
C. `1/5`
D. `2/3`

Answer

B

Explanation

Rolling is rotation about point of contact. Applying impulse momentum equation about `P`.

`J(R+h)=I_(p)omega` ………i
and `J=mv`………ii
As sphere rolls `v=omegaR` and `I=2/5mR^(2)mR^(2)=7/5 mR^(2)`
After solving we get `h/R=2/5`