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

For rolling without slipping.
`a=(gsintheta)/(1+(I)/(mR^(2)))`
For solid sphere, `I=(2)/(5)mR^(2)`
`a=(5)/(7)gsintheta`
For slipping down on inclined plane without rolling
`F=ma_(1)=mgsintheta`
`a_(1)=gsintheta`

Ratio `implies(a)/(a_(1))=(5)/(7)`