When a solid sphere rolls without slipping down an inclined plane making an angle `theta` with the horizontal, the acceleration of its centre of mass is `a`. If the same sphere slides without friction, its.

Options

A. `(7)/(2) a`
B. `(5)/(7) a`
C. `(7)/(5) a`
D. `(5)/(2) a`

Answer

C

Explanation

( c) Acceleration of the solid sphere when it rolls without slipping down an inclined plane is.
`a = (g sin theta)/(1 + (I)/(MR)^2)`
For a solid sphere, `I = (2)/(5) MR^2`
:. `a = (g sin theta)/(1 + (2)/(5)) g sin a`
Acceleration of the same sphere when it slides without friction down an same inclined plane is.
`a' = g sin theta`
Divide (ii) by (i), we get, `(a')/(a) = (7)/(5)` or `a' = (7)/(5) a`.