A) solid sphere
B) hollow sphere
C) disc
D) ring
Correct Answer: C
Solution :
Let v be the moment of inertia of the body. Then total \[KE=\frac{1}{2}\,\,m{{v}^{2}}+\frac{1}{2}I\,{{\omega }^{2}}\] \[KE\,\,=\,\,\frac{1}{2}m{{v}^{2}}\,+\,\frac{1}{2}I\,\,\frac{{{v}^{2}}}{{{R}^{2}}}\,\,\left( \omega =\frac{v}{R} \right)\] According to energy conservation loss in KE = gain in PE. \[or\,\,\frac{1}{2}\,\left( m+\frac{I}{{{R}^{2}}} \right){{v}^{2}}\,=\,mgh\,\,=\,\,mg\,\left( \frac{3{{v}^{2}}}{4g} \right)\] Solving this, we get \[I\,\,=\,\,\frac{1}{2}\,\,m{{R}^{2}}\] i.e., the solid body is a disc
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