Question

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $0.36\, kg$ and $0.72 \, kg$. Taking $g=10\, ms ^{-2}$, find the work done (in Joule) by string on the block of mass $0.36\, kg$ during the first second after the system is released from rest.

Answer 1

$a=\frac{\text { Net pulling force }}{\text { Total mass }}=\frac{0.72 \,g-0.36\, g}{0.72+0.36}=\frac{g}{3}$
$s=\frac{1}{2} a t^{2}=\frac{1}{2}\left(\frac{g}{3}\right)(1)^{2}=\frac{g}{6}$

$ T-0.36 \,g=0.36 \,a=0.36 \frac{g}{3}$
$\therefore T=0.48\, g$
Now, $ W_{T}=T S \cos 0^{\circ}$
(on $0.36\, kg$ mass)
$=(0.48 g)\left(\frac{g}{6}\right)(1)$
$=0.08\left(g^{2}\right)=0.08(10)^{2}=8 \,J$