Question

A block of mass $m=2\text{kg}$ on a smooth inclined plane at an angle ${30}^{\circ }$ is connected to a second block of mass $m_2=3\text{kg}$ by a cord passing over a frictionless pulley as shown in fig. The acceleration of each block (in ${\text{m/s}}^2$) is
(assume $g=10{\text{m/sec}}^2$)

Answer 1

NLM for $m$ and $m_2$ gives
$m_{2}g-T=m_{2}a.....\left(1\right)$
$T-mg\sin \theta =ma.....\left(2\right)$
Adding (1) and (2)
$m_{2}g-mg\sin \theta =(m+m_2)a$

$a=\frac{F_{net}}{m}=\frac{30-10}{5}=4{\text{m/s}}^2$