Question

In the figure shown $C$ is a fixed wedge. A block $B$ is kept on the inclined surface of the wedge $C$. Another block $A$ is inserted in a slot in the block $B$ as shown in figure. A light inextensible string passes over a light pulley which is fixed to the block $B$ through a light rod. One end of the string is fixed and other end of the string is fixed to $A.S$ is a fixed support on the wedge. All the surfaces are smooth. Masses of $A$ and $B$ are same. Then the magnitude of acceleration of $A$ is $\frac{\sqrt{x}}{3}m/s^2$. Then $x$ is $(\sin {37}^{\circ }=3/5)$.

Answer 1

Lets find relation between accelerations of two blocks using string constrain.

$x+y=L$

Differentiating twice w.r.t time.

$a_A+a_B=0$

let $a$ be the magnitude of acceleration for block $B$.

$2mg\sin \theta -T=2ma\to \left(1\right)$

For block $A$

$T-mg\cos \theta =ma\to \left(2\right)$

From here we can get,

$T=\frac{14mg}{15}$

acceleration of $A=\frac{4}{3}m{s}^{-2}$

acceleration of $B=\frac{4}{3}m{s}^{-2}$

So, resultant acceleration of $A$ is

$a_A=\sqrt{{\left(\frac{4}{3}\right)}^2+{\left(\frac{4}{3}\right)}^2}$

$a_A=\frac{\sqrt{32}}{3}m{s}^{-2}$