Question

A block is released from the top of an inclined plane of inclination `theta`. Its velocity at the bottom of plane is `v`. If it slides down a rough inclined plane of the same inclination , its velocity at bottom is `v//2`. The coefficient of friction is
A. `(3)/(4) cos theta`
B. `(1)/(4) cos theta`
C. `(1)/(4) tan theta`
D. `(3)/(4) tan theta`

Answer 1

Correct Answer - D
`v^(2) = 2 g sin theta s` (i)
`((v)/(2))^(2) = 2 ( g sin theta - mu g cos theta) s` (ii)
`(1)/(4) xx 2 g sin theta xx s = 2(g sin theta - mu g cos theta) s`
`(sin theta)/(4) ( sin theta - mu cos theta ) rArr mu = (3)/(4) tan theta`