Physics - NLM Question with Solution | TestHub

Let $T_2$ be the tension in the string over pulley $P_2$.
Since the 100 gm mass stays at rest
$$T_2=0.1g=1\mathrm{N}.$$
For the 200 gm mass
$$0.2g-T_2=0.2a_2$$
gives
$$a_2=5m/{\mathrm{s}}^2$$ down.
The string constraint
$$x_{100}+x_{200}=2x_{P_2}$$
with the 100 gm mass fixed gives
$$a_{P_2}=2.5m/{\mathrm{s}}^2$$ down.
$P_2$ is light, so the tension over fixed pulley $P_1$ is
$$T_1=2T_2=2\mathrm{N}.$$
$m_1$ moves up with $2.5$ m/s²
$$T_1-m_{1}g=m_1(2.5)$$
so
$$m_1=\frac{2}{12.5}=0.16\mathrm{kg}$$ = $160$ gm.
Option B.