Question

A disc of mass $m_0$ rotates freely about a fixed horizontal axis passing through its center. A thin cotton pad is fixed to its rim, which can absorb water. The mass of water dripping onto the pad per unit time is $\mu$. After what time will the angular velocity of the disc get reduced to half its initial value?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$L=I_0{\omega }_0=\frac{I{\omega }_0}{2};2I_0=I$ or $2\left(\frac{1}{2}{m}_0{r}^2\right)=\frac{1}{2}{m}_0{r}^2+\left(\mu t\right)r^2$

$\therefore t=\frac{m_0}{2\mu }$