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)/g)`
D. `-g/(sqrt(l^(2)+1))`

Answer

A

Explanation

Let the acceleration be a
Horizontal force `= ma cos theta`
`ma cos theta = mg sin theta`
`a = g tantheta`
`sin theta=1/l`
` implies tan theta=1/sqrt(l^(2)-1)`
` therefore a=g/sqrt(l^(2)-1)`.