A) 24 h
B) 48 h
C) 6 h
D) 12 h
Correct Answer: C
Solution :
Under the absence of external torque on a rotating body, angular momentum remains constant. That is \[J=I\omega =cons\tan t\] \[\therefore \] \[{{I}_{1}}{{\omega }_{1}}={{I}_{2}}{{\omega }_{2}}\] where\[I\]is moment of inertia and co the angular velocity. Also, \[\omega =\frac{2\pi }{T}\] \[\therefore \] \[\left( \frac{2}{5}MR_{1}^{2} \right)\left( \frac{2\pi }{24} \right)=\left( \frac{2}{5}MR_{2}^{2} \right)\left( \frac{2\pi }{{{T}_{2}}} \right)\] \[\Rightarrow \] \[\frac{R_{1}^{2}}{R_{2}^{2}}=\frac{24}{{{T}_{2}}}\] \[\Rightarrow \] \[{{\left( \frac{{{R}_{1}}\times 2}{{{R}_{1}}} \right)}^{2}}=\frac{24}{{{T}_{2}}}\] \[\Rightarrow \] \[{{T}_{2}}=\frac{24}{4}=6\,h\]
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