A) \[\frac{2M}{5}\frac{(R_{2}^{5}-R_{1}^{5})}{(R_{2}^{5}-R_{1}^{3})}\]
B) \[\frac{2M}{5}\frac{(R_{2}^{5}-R_{1}^{5})}{(R_{2}^{3}-R_{1}^{3})}\]
C) \[\frac{4M}{5}\frac{(R_{2}^{5}-R_{1}^{5})}{(R_{2}^{3}-R_{1}^{3})}\]
D) \[\frac{4M}{3}\frac{(R_{2}^{5}-R_{1}^{5})}{(R_{2}^{3}-R_{1}^{3})}\]
Correct Answer: A
Solution :
[a] \[\rho =\frac{M}{\frac{4}{3}\pi (R_{2}^{3}-R_{1}^{3})}\] \[{{I}_{shell}}=\frac{2}{5}{{M}_{2}}R_{2}^{2}-\frac{2}{5}{{M}_{1}}R_{1}^{2}\] ?. (1) \[{{M}_{2}}=\rho \times \frac{4}{3}\pi R_{2}^{3}\] \[=\frac{MR_{2}^{3}}{(R_{2}^{3}-R_{1}^{3})};\,{{M}_{1}}=\frac{MR_{1}^{3}}{R_{2}^{3}-R_{1}^{3}}\] Putting values of \[{{M}_{1}}\]and \[{{M}_{2}}\]in eq. (1), \[{{I}_{shell}}=\frac{2M}{5}\frac{(R_{2}^{5}-R_{1}^{5})}{(R_{2}^{3}-R_{1}^{3})}\]You need to login to perform this action.
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