Question

Consider the situation shown in figure . All the surfaces are friction-less and the string and the pulley are light. Find the magnitude of the acceleration of the two block.

Answer 1

$\sin {\theta }_1=4/5$ $g\sin {\theta }_1-(a+T)=0$ $T-g\sin {\theta }_2-a=0$
$\sin {\theta }_2=3/5$ $\Rightarrow g\sin g{\theta }_1=a+T$ $\Rightarrow T=g\sin {\theta }_2+a$ $\Rightarrow T+a-g\sin {\theta }_1=0$
From eqn (i) and (ii) $g\sin {\theta }_2+a+a-g\sin {\theta }_1=0$
$\Rightarrow 2a=g\sin {\theta }_1-g\sin {\theta }_2=g(\frac{4}{5}-\frac{3}{5})=g/5$$\Rightarrow =\frac{g}{5}\times \frac{1}{2}=\frac{g}{10}$