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

Explanation

Rolling without slipping
`a_(1)=(g sin theta)/(1+(k^(2))/(R^(2)))=(gsin theta)/(1+(2)/(5))=(5)/(7) g sin theta`
Slipping without rolling
`a_(2)= g sin theta`
`(a_(1))/(a_(2))=(5)/(7)`