A) \[\frac{1}{3}M{{L}^{2}}\]
B) \[\frac{3}{2}M{{L}^{2}}\]
C) \[\frac{3}{4}M{{L}^{2}}\]
D) \[M{{L}^{2}}\]
Correct Answer: C
Solution :
From the triangle BCD \[{{(CD)}^{2}}={{(BC)}^{2}}-{{(BD)}^{2}}\] \[={{L}^{2}}-{{\left( \frac{L}{2} \right)}^{2}}\] \[{{x}^{2}}=\frac{3{{L}^{2}}}{4}\] \[\Rightarrow \] \[x=\frac{\sqrt{3}}{2}L\] Moment of inertia of system along the side AB \[{{I}_{sys.}}={{I}_{1}}+{{I}_{2}}+{{I}_{3}}\] \[=M\times {{(0)}^{2}}+M\times {{(x)}^{2}}+M\times {{(0)}^{2}}\] \[=M{{x}^{2}}=M{{\left( \frac{\sqrt{3}L}{2} \right)}^{2}}=\frac{3M{{L}^{2}}}{4}\]You need to login to perform this action.
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