Question

Find the acceleration of each block in the situation shown in the figure. All the surfaces are smooth and the pulleys and strings are light.

Answer 1

The distance covered by mass $m$ in any time interval will be equal to twice the distance covered by mass $2m$ in the same time interval. therefore, acceleration of mass $m$ will be twice that of the mass $2m$.

Let acceleration of mass $2m$ is $a$. Then acceleration of mass $m$ will be$2a$.

The force equation for mass $m$ is,

$T=m\times 2a$

The force equation for mass $2m$ is,

$2T=2m\left(g-a\right)$

$2\times 2ma=2mg-2ma$

$a=\frac{g}{3}$

Thus acceleration of mass $m$ will be $\frac{2g}{3}$ and acceleration of mass $2m$ will be$\frac{g}{3}$.