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6.System of Particles and Rotational Motion
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A disc of mass $m$ and radius $r$ is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass $m$ is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height $h$, is .....
A
$\sqrt{2 g h}$
B
$\sqrt{\frac{2}{3} g h}$
C
$2 \sqrt{\frac{g h}{3}}$
D
$\frac{1}{2} \sqrt{3 g h}$
Solution
(c)
Using Mechanical energy conservation
$m g h=\frac{1}{2} m v^2+\frac{1}{2}\left(\frac{1}{2}\right) m r^2 \cdot \frac{v^2}{r^2}$
$m g h=\frac{3}{4} m v^2$
$v^2=\frac{4 g h}{3}$
$v=\sqrt{\frac{4 g h}{3}}$
Standard 11
Physics
