A block moves down a smooth plane of inclination `theta`. Its velocity on reaching the bottom is v. If it slides down a rough inclined plane some inclination, its velocity on reaching the bottom is v/n, where n is a number greater than 0. The coefficient of friction is given by:

Options

A. `mu = tan theta (1- 1/n^(2))`
B. `mu = cot theta (1-1/n^(2))`
C. `mu = tan theta (1- 1/n^(2))^(1//2)`
D. `mu = cot theta (1- 1/n^(2))^(1//2)`

Answer

A

Explanation

`v^(2) = 2g sin theta xx l`
`v^(2)/n^(2) = 2(g sin theta - mu g costheta)l`
`sin theta(1-1/n^(2)) = mu cos theta`
`mu = tan theta (1-1/n^(2))`