Question

In the figure shown, pulley and cord have negligible mass and friction. The system is balanced with equal masses $M$ on each side as shown (solid line), and then a small mass $m$ is gently placed to one block at position $A$. The combined masses accelerate through a certain distance $h$, and then mass $m$ is gently removed at position $B$ and two equal masses then move on with constant speed $v.$ If the value of $v$ is $10\alpha$ (in $cm/s$ ), then find the value of $\alpha$.
(Given: $m=250g,M=1kg,h=16.2cm$ and $g=10m/s^2$ )

Answer 1

Answer: 6

$a=\frac{mg}{2M+m}$
$v^2=2\left(\frac{mg}{2M+m}\right)\times h$
$=2\left[\frac{0.25\times 10}{2+0.25}\right]\times 16.2\times 10^{-2}$
$v^2=\frac{5\times 16.2\times 10^{-2}}{0.25}$
$v=0.6m/s$