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 :
\[2R=\sqrt{3}a\] \[\frac{2R}{\sqrt{3}}=a\] \[I=\frac{mass{{\left( side \right)}^{2}}}{6}\] \[=\left( \frac{M}{\frac{4}{3}\pi {{R}^{3}}} \right){{a}^{3}}\frac{4{{R}^{2}}}{3}\frac{1}{6}\] \[=\frac{3M}{4\pi {{R}^{3}}}\frac{8{{R}^{3}}}{3\sqrt{3}}\frac{4{{R}^{2}}}{3\times 6}\] \[=\frac{8M{{R}^{2}}}{18\sqrt{3}\pi }=\frac{4M{{R}^{2}}}{\pi 9\sqrt{3}}\]You need to login to perform this action.
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