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

(a) Acceleration of sphere when it is slipping down the incline, `a_(slipping) = g sin theta`
Acceleration of sphere when it is rolling down
`a_("rolling") = (g sin theta)/(1 + (K^2)/(r^2)) = (5)/(7) g sin theta`
Hence required ratio `(a_("rolling"))/a_("slipping") = (5)/(7)`.