A) \[\frac{2{{\pi }^{2}}{{n}^{2}}{{R}^{2}}}{5C}\]
B) \[\frac{{{\pi }^{2}}{{n}^{2}}{{R}^{2}}}{5C}\]
C) \[\frac{2{{\pi }^{2}}{{n}^{2}}R}{5C}\]
D) \[\frac{{{\pi }^{2}}{{n}^{2}}R}{5C}\]
Correct Answer: A
Solution :
| the rotational K.E. of the sphere \[K=\frac{1}{2}I{{\omega }^{2}}\]\[=\frac{1}{2}\left( \frac{2}{5}M{{R}^{2}} \right){{\left( 2\pi n \right)}^{2}}=\left( \frac{4{{\pi }^{2}}}{5}{{n}^{2}} \right)M{{R}^{2}}\] |
| Kinetic energy used to raise the temperature,\[=\frac{50}{100}\left[ \frac{4{{\pi }^{2}}{{n}^{2}}}{5}M{{R}^{2}} \right]\] |
| Let \[\Delta T\]be the raise the temperature, then \[MC\Delta T=\frac{2{{\pi }^{2}}{{n}^{2}}}{5}M{{R}^{2}}\] |
| \[\therefore \Delta T=\frac{2{{\pi }^{2}}{{n}^{2}}{{R}^{2}}}{5C}\] |
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