A) \[\frac{4M{{R}^{2}}}{9\sqrt{3\pi }}\]
B) \[\frac{4M{{R}^{2}}}{3\sqrt{3\pi }}\]
C) \[\frac{M{{R}^{2}}}{32\sqrt{2\pi }}\]
D) \[\frac{M{{R}^{2}}}{16\sqrt{2\pi }}\]
Correct Answer: A
Solution :
[a] Here \[a=\frac{2}{\sqrt{3}}R\] Now, \[\frac{M}{M'}=\frac{\frac{4}{3}\pi {{R}^{3}}}{{{a}^{3}}}\] \[=\frac{\frac{4}{3}\pi {{R}^{3}}}{{{\left( \frac{2}{\sqrt{3}}R \right)}^{3}}}=\frac{\sqrt{3}}{2}\pi .\] \[M'=\frac{2M}{\sqrt{3}\pi }\] Moment of inertia of the cube about the given axis, \[I=\frac{M'{{a}^{2}}}{6}\] \[=\frac{\frac{2M}{\sqrt{3}\pi }\times {{\left( \frac{2}{\sqrt{3}}R \right)}^{2}}}{6}=\frac{4M{{R}^{2}}}{9\sqrt{3}\pi }\]You need to login to perform this action.
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