Question

In the arrangement shown in figure, $m_{1}=1\, kg , m_{2}=2 \,kg$. Pulleys are massless and strings are light. For what value of $M$ (in $kg$ ) the mass $m_{1}$ moves with constant velocity? (Neglect friction)

Answer 1

$m_{1}=1 \,kg $
$m_{2}=2 \,kg $
$a_{m_{1}}=\frac{g}{3}$
$m_{1}$ will move with constant velocity if $a=0$.
So, downward acceleration should be $\frac{g}{3}$.
$\Rightarrow T=\frac{4 g}{3} $
$\therefore M \frac{g}{3}=\frac{8 g}{3} $
$\Rightarrow M=8 \,kg$