The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle `theta` without slipping and slipping down the incline without rolling is

Options

A. `5 : 7`
B. `2 : 3`
C. `2 : 5`
D. `7 : 5`

Answer

A

Explanation

Acceleration of the solid sphere slipping down the incline without rolling is
`a_("slipping") = g sin theta " " …. (i)`
Acceleration of the solid sphere rollind down the incline without slipping is
`a_("rolling") = (g sin theta)/(1 + (k^(2))/(R^(2))) = (a sin theta)/(1 + 2/5) ( because` For solid sphere , `(k^2)/(R^2) = (2)/(5)`)
`= (5)/(7) g sin theta " " ... (ii)`
Divide eqn. (ii) by eqn.(i) , we get `(a_("rolling"))/(a_("slipping")) = (5)/(7)`