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The ratio of the accelerations for a sol...

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`

Text Solution

Verified by Experts

The correct Answer is:
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`
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