Question

A block of mass $m_1=2kg$ is kept on a smooth horizontal table. Another block of mass $m_2=1kg$ is connected to $m_1$ by a light inextensible string passing over a smooth pulley as shown in the figure. If the blocks are released, what will be the $\left(a\right)$ acceleration of each block $\left(b\right)$ tension in the string?

Answer 1

From the $F.B.D$ of $m_1$
$N=m_{1}g$ ...$\left(1\right)$
$T=m_{1}a$ ...$\left(2\right)$
From the $F.B.D$ of $m_2$
$m_{2}g-T=m_{2}a$ ...$\left(3\right)$

$\left(a\right)$

From $\left(2\right)$ and $\left(3\right)$
$m_{2}g=(m_1+m_2)a$

$\therefore a=\frac{m_{2}g}{m_1+m_2}$ ...$\left(4\right)$
$=\frac{1}{3}\times 9.8m/s^2=3.26m/s^2$

$\left(b\right)$
From $\left(2\right)$ and $\left(4\right)$
$T=m_{1}a=\frac{m_1{m}_2}{m_1+m_2}g=\frac{2\times 1}{2+1}\times 9.8N=6.52N$