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

As solid sphere rolling without slipping down an inclined plane

In this case, `a_(1)=(g sin theta)/(1+(K^(2))/(R^(2)))=(g sin theta)/(1+((2//5)R^(2))/(R^(2)))`
`" " [therefore " for solid sphere, "K^(2)=(2)/(5)R^(2)]`
`=(g sin theta)/(7//5) rArr a_(1)=(5)/(7)g sin theta`
For a sphere slipping down an inclined plane,
`rArr" "a_(2)= g sin theta rArr (a_(1))/(a_(2))=(5//7g sin theta)/(g sin theta)`
`rArr" "(a_(1))/(a_(2))=(5)/(7)`