A) \[\frac{5}{2}m{{\ell }^{2}}\]
B) \[\frac{5}{4}m{{\ell }^{2}}\]
C) \[\frac{3}{2}m{{\ell }^{2}}\]
D) \[\frac{5}{3}m{{\ell }^{2}}\]
Correct Answer: B
Solution :
[b] Moment of Inertia of each of rod AC and BC about the given axis OO' is \[{{I}_{AC}}={{I}_{BC}}=\frac{m{{\ell }^{2}}}{3}{{\sin }^{2}}60{}^\circ =\frac{m{{\ell }^{2}}}{4}\] and M.I. of rod AB about the given axis OO' is \[{{I}_{AB}}=m{{\left( \frac{\ell \sqrt{3}}{2} \right)}^{2}}=\frac{3}{4}m{{\ell }^{2}}\] Hence, \[I={{I}_{AC}}+{{I}_{BC}}+{{I}_{AB}}=\frac{m{{\ell }^{2}}}{4}+\frac{m{{\ell }^{2}}}{4}+\frac{3}{4}m{{\ell }^{2}}=\frac{5}{4}m{{\ell }^{2}}\]You need to login to perform this action.
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