Question

A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given $m=8kg,M=16kg$
Assume all the surfaces shown in the figure to be frictionless.

• A. $\frac{4}{3}g$
• B. $\frac{6}{5}g$
• C. $\frac{3}{5}g$
• D. $\frac{2}{3}g$

Answer 1

Answer: (D)

Let acceleration of wedge is $a_1$ and acceleration of block w.r.t. wedge is $a_2$

$N\cos 60^{\circ }=M{a}_1=16a_1$
$\Rightarrow N=32a_1$
F.B.D. of block w.r.t wedge

$\perp$ to incline
$N=8g\cos 30^{\circ }-8a_1\sin 30^{\circ }$
$\Rightarrow 32a_1=4\sqrt{3}g-4a_1$
$\Rightarrow a_1=\frac{\sqrt{3}}{9}g$
Along incline
$8g\sin 30^{\circ }+8a_1\cos 30^{\circ }=m{a}_2=8a_2$
$a_2=g\times \frac{1}{2}+\frac{\sqrt{3}}{9}g.\frac{\sqrt{3}}{2}=\frac{2g}{3}$