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

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 μ . After what time will the angular velocity of the disc get reduced to half its initial value?

TestHub · Accepted Answer

No external torque about the axis, so L is conserved

Half the angular velocity means double the moment of inertia

$2 (\frac{1}{2} m_{0} r^{2}) = \frac{1}{2} m_{0} r^{2} + (μ t) r^{2}$

$t = \frac{m _{0}}{2 μ}$

Answer: D

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