A) \[\frac{1}{3}M{{L}^{2}}\]
B) \[\frac{3}{2}M{{L}^{2}}\]
C) \[\frac{3}{4}M{{L}^{2}}\]
D) ML2
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 \[{{I}_{sys.}}={{I}_{1}}+{{I}_{2}}+{{I}_{3}}\] \[=m\times {{(0)}^{2}}+m\times {{(x)}^{2}}+m\times {{(0)}^{2}}\] \[=m{{x}^{2}}=m{{\left( \frac{\sqrt{3L}}{2} \right)}^{2}}\] \[=\frac{3m{{L}^{2}}}{4}\]You need to login to perform this action.
You will be redirected in
3 sec