A body of mass `m` is launched up on a rough inclined plane making an angle `45^(@)` with horizontal If the time of descent between plane and body is

Options

A. `(2)/(5)`
B. `(3)/(5)`
C. `(3)/(4)`
D. `(4)/(5)`

Answer

b

Explanation

`t_(A) = sqrt((2s)/(a_(A))) rArr t_(D) = sqrt((2s)/(a_(D))),t_(A) = (1)/(2) t_(D)`
`sqrt((2s)/(g sin theta + mu g cos theta))= (1)/(2) sqrt((2s)/(g sin theta - mu g cos theta))`
`4g sin theta - 4 mu g cos theta= g sin theta + mu g cos theta`
`5g sin theta - 5 mu g cos theta` or `mu = (3)/(5) tan theta = (3)/(5) tan theta = (3)/(5)`
`( :' theta = 45^(@))`