question_answer

Three particles, each of mass m grams situated at the vertices of an equilateral triangle ABC of side I cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of A BC. in gram \[-c{{m}^{2}}\]units will be

A) \[(3/4)\,m{{l}^{2}}\]

B) \[2\,m{{l}^{2}}\]

C) \[(5/4)\,m{{l}^{2}}\]

D) \[(3/2)\,m{{l}^{2}}\]   

Correct Answer: C

Solution :

 Moment of inertia of the system about AX is given by \[MI={{m}_{A}}r_{A}^{2}+{{m}_{B}}r_{B}^{2}+{{m}_{C}}r_{C}^{2}\] \[MI=m{{(0)}^{2}}+m{{(l)}^{2}}+m{{(l\sin {{30}^{o}})}^{2}}\] \[=m{{l}^{2}}+\frac{m{{l}^{2}}}{4}=\frac{5}{4}m{{l}^{2}}\]