A block is sliding along an inclined plane as shown in figure . If the acceleration of chamber is `a` as shown in figure. The time required to cover a distance `L` along inclined is

Options

A. `sqrt((2L)/(g sin theta - a cos theta))`
B. `sqrt((2L)/(g sin theta + a sin theta))`
C. `sqrt((2L)/(g sin theta + a cos theta))`
D. `sqrt((2L)/(g sin theta))`

Answer

C

Explanation

FBD of m w.r.t chamber
Relative acceleration along the inclined plane
`a_(r ) = (m a cos theta + m g sin theta)/(m)`
`= (a cos theta + g sin theta)`
`t = sqrt((2s)/(a_(r))) = sqrt((2L)/(a cos theta + g sin theta))`