Question

A disc of mass $m_{0}$ rotates freely about a fixed horizontal axis through its centre. A thin cotton pad is fixed to its rim, which can absorb water. The mass of water dripping onto the pad is $\mu$ per second. After what time will the angular velocity of the disc get reduced to half of its initial value ?

• A. $\frac{2 m_{0}}{\mu}$
• B. $\frac{3 m_{0}}{\mu}$
• C. $\frac{m_{0}}{\mu}$
• D. $\frac{m_{0}}{2 \mu}$

Answer 1

Answer: (D)

Mass of cotton pad after time $t$ is
$m=\mu t$
By conservation of angular momentum,
$\frac{m_{0} r^{2}}{2} \omega =\left[\frac{m_{0} r^{2}}{2}+\mu t r^{2}\right] \frac{\omega}{2} $
$\Rightarrow m_{0} r^{2} =\frac{m_{0} r^{2}}{2}+\mu t r^{2} $
$\Rightarrow t =\frac{m_{0}}{2 \mu}$