Question

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

Answer 1

Correct Answer - A
`a_("slipping") = g sin theta` (without rolling)
`a_("rolling") = (g sin theta)/(1+K^(2)//R^(2))` (without slipping)
`:. (a_("slipping"))/(a_("rolling")) = 1 + (K^(2))/(R^(2)) = 1+ (2//5R^(2))/(R^(2)) = (7)/(5)`
Hence, `a_("rolling") : a_("slipping") = 5:7`