The ratio of the acceleration 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_("slipping") = g sin theta , a_("rolling") = (g sin theta)/(1 + (k^(2))/(r^(2)))`
For sphere,` k = sqrt((2)/(5))r " " therefore k^(2) = (2)/(5) r^(2)`
So, ` a_("rolling") = (g sin theta)/( 1 + (2)/(5)) = (5)/(7) g sin theta`
`therefore (a_("rolling"))/(a_("slipping")) = ((5)/(7) g sin theta)/(g sin theta) = (5)/(7)`