A uniform disc of mass m_0 rotates freely about a fixed horizonta… - Vidyadip

Question

A uniform disc of mass $m_0$ rotates freely about a fixed horizontal axis passing through its centre. 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 ?

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Answer

$\mathrm{L}=\mathrm{I}_{0} \omega_{0}=\frac{\mathrm{I} \omega_{0}}{2} \Rightarrow 2 \mathrm{I}_{0}=\mathrm{I}$

$\Rightarrow 2\left(\frac{1}{2} m_{0} r^{2}\right)=\frac{1}{2} m_{0} r^{2}+(\mu t) r^{2} \Rightarrow t=\frac{m_{0}}{2 \mu}$

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