Question

Consider the situation shown in figure. All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of the acceleration of the two blocks.

Answer 1

Given, Reset as

Here $sin{\theta }_1=\frac{4}{5}$

We know , g $sin{\theta }_1-(a+T)=0$

$\Rightarrow gsin{\theta }_1+a+T$ ...(i)

Again , $sin{\theta }_2=\frac{3}{5}$

We know,$T-gsin{\theta }_2-a=0$

$\Rightarrow T=gsin{\theta }_2+a...\left(ii\right)$

From equations (i) and (ii),

$gsin{\theta }_2+a+a-gsin{\theta }_1=0$

$\Rightarrow 2a=gsin{\theta }_1-gsin{\theta }_2$

$\Rightarrow a=\frac{g}{5}\times \frac{1}{2}$

$=\frac{g}{10}$