Question

In terms of masses $m_1$, $m_2$ and $g$ find the acceleration of both the blocks shown in Fig. .Neglects all friction and masses of the pulley

Answer 1

Given,

Acceleration of lock $m_1$ is$a_1$.

Acceleration of lock $m_2$ is$a_2$.

String is non-stretchable

$a_2=2a_1.......\left(1\right)$

$m_{2}g-2T_1=m_2{a}_2....\left(2\right)$

$T_1=m_1{a}_1......\left(3\right)$

From (1), (2) and (3)

$a_2=\frac{m_{2}g}{m_1+m_2}$ and $a_1=\frac{m_{2}g}{2(m_1+m_2)}$

Hence, acceleration of lock $m_{1}is\frac{m_{2}g}{2(m_1+m_2)}$ and acceleration of lock $m_{2}is\frac{m_{2}g}{(m_1+m_2)}$