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 $m =8\, kg , M =16 \,kg$
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}= Ma _{1}=16 a _{1} $
$\Rightarrow N =32 a _{1}$
F.B.D. of block w.r.t wedge

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