Question

A block of mass $m$ is placed on a prism of mass $M$. The inclined surface is smooth and inclination with horizontal is $\theta$. The horizontal surface is sufficiently rough to prevent slipping of prism. The body of mass $m$ is coming down the inclined face. Then

• A. Acceleration of body along the inclined surface is $g\sin \theta$
• B. Frictional force is $\frac{1}{2}mg\sin 2\theta$
• C. Maximum frictional force is $\frac{mg}{2}$
• D. Frictional force will be maximum when $\theta ={45}^{\circ }$

Answer 1

Answer: (A), (B), (C), (D)

Frictional force will be maximum when $\theta ={45}^{\circ }$

From FBD of the block
$N=mg\cos \theta$
$ma=mg\sin \theta \Rightarrow a=g\sin \theta$



From FBD of prism, as prism is in rest
$F_s=N\sin \theta =mg\cos \theta \times \sin \theta =\frac{mg}{2}\sin 2\theta$
If $F_s\to$ maximum,$(2\theta ={90}^{\circ }\Rightarrow \theta ={45}^{\circ })$
$\therefore (F_s{)}_{\text{max}}=\frac{mg}{2}$