An object is kept on a smooth inclined plane of height 1 unit and length l units. The horizontal acceleration to be imparted to the inclined plane so that the object is stationary relative to the incline is

Options

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

Answer

C

Explanation

for the object to remain stationary relative to the incline figure clearly shows that
` m a cos theta = mg sin theta `
` or a= g tan theta `
As ` sin theta = (1)/(l ) `
` therefore tan theta = ( 1)/(sqrt(l^2-1))`
` therefore a= ( g)/( sqrt(l^2 -1))`