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 gets reduced to half of its initial value?

• A. $\frac{2m_0}{\mu }$
• B. $\frac{3m_0}{\mu }$
• C. $\frac{m_0}{\mu }$
• D. $\frac{m_0}{2\mu }$

Answer 1

The correct option is D $\frac{m_0}{2\mu }$

Mass of cotton pad after time is
$m=\mu t$
By conservation of angular momentum
$\frac{m_0{r}^2}{2}\omega =[\frac{m_0{r}^2}{2}+\mu t{r}^2]\frac{\omega }{2}$
$\Rightarrow m_0{r}^2=\frac{m_0{r}^2}{2}+\mu t{r}^2$
$\Rightarrow t=\frac{m_0}{2\mu }$