A) \[\frac{M{{L}^{2}}}{24}\]
B) \[\frac{M{{L}^{2}}}{12}\]
C) \[\frac{M{{L}^{2}}}{6}\]
D) \[\frac{\sqrt{2}M{{L}^{2}}}{24}\]
Correct Answer: B
Solution :
Since rod is bent at the middle, so each part of it will have same length \[\left( \frac{L}{2} \right)\] and mass \[\left( \frac{M}{2} \right)\] as shown. |
Moment of inertia of each part through its one end \[=\frac{1}{3}\left( \frac{M}{2} \right){{\left( \frac{L}{2} \right)}^{2}}\] |
Hence, net moment of inertia through its middle point O is |
\[I=\frac{1}{3}\left( \frac{M}{2} \right){{\left( \frac{L}{2} \right)}^{2}}+\frac{1}{3}\left( \frac{M}{2} \right){{\left( \frac{L}{2} \right)}^{2}}\] |
\[=\frac{1}{3}\left[ \frac{M{{L}^{2}}}{8}+\frac{M{{L}^{2}}}{8} \right]=\frac{M{{L}^{2}}}{12}\] |
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