| Suppose in gravity free space 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 \[\mu \] kg per second. After what time will the angular velocity of the disc get reduced to half of its initial value? |
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A) \[2{{m}_{0}}/\mu \]
B) \[3{{m}_{0}}/\mu \]
C) \[{{m}_{0}}/\mu \]
D) \[{{m}_{0}}/2\mu \]
Correct Answer: D
Solution :
Conservation of angular momentum \[\Rightarrow \frac{{{\omega }_{0}}}{2}\left[ (\mu t){{R}^{2}}+\frac{{{m}_{0}}{{R}^{2}}}{2} \right]=\frac{{{m}_{0}}{{R}^{2}}}{2}={{\omega }_{0}}\] \[\Rightarrow t=\frac{{{m}_{0}}}{2\mu }\]
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