Question

A block, of mass M, is kept on a smooth inclined plane, of incline ‘1 in l ’. When the inclined plane is given a horizontal acceleration a, it is observed that the block says stationary relative to the ‘incline’. The acceleration, a, equals

(1) \(\frac{g}{\sqrt{l^2+1}}\)

(2) \(\frac{g}{\sqrt{l^2-1}}\)

(3) \(g(\frac{1}{l})\)

(4) \(g\frac{(\sqrt{l^2-1})}{l}\)

Answer 1

 (2) \(\frac{g}{\sqrt{l^2-1}}\)

For the given incline, we have

Sin θ = 1/l

Cos θ = \((\frac{\sqrt{l^2-1}}{l})\)

The acceleration, of the block, down the inclined plane is g sin θ. The component of the horizontal acceleration, a, of the ‘incline’, along the inclined plane, is a cos θ. 

The block will remain stationary, relative to the incline, if

a cos θ = g sin θ 

or a = g tan θ 

= g \(\frac{g}{\sqrt{l^2-1}}\)