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: $m=250 \,g, M=1 \,kg , h=16.2\, cm$ and $g=10\, m / s ^{2}$ )

Answer 1

$ a =\frac{m g}{2 M+m} $
$ v^{2} =2\left(\frac{m g}{2 M+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 =0.6\, m / s $