The horizontal acceleration that should be given to a smooth inclined plane of angle `sin^(-1)((1)/(l))` to keep an object stationary on the plane relative to the inclined plane is .

Options

A. `g/sqrt(l^(2)-1)`
B. `g sqrt(l^(2)-1)`
C. `sqrt(l^(2)-1)/gN`
D. `g/sqrt(l^(2)+1)`

Answer

A

Explanation

If block is at rest w.r.t. wedge
`mg sin theta=ma cos theta`
`:. A=g tan theta`
`because sin theta=1/l`
`:.tan theta=1/sqrt(l^(2)-1)`
`:.a=g/sqrt(l^(2)-1)`