question_answer

Three point masses \[{{m}_{1}},\,\,{{m}_{2}},\,\,{{m}_{3}}\] are located at the vertices of an equilateral triangle of length a. The moment of inertia of the system about an axis along the altitude of the triangle passing through m1, is

A)  \[\left( {{m}_{2}}+{{m}_{3}} \right)\frac{{{a}^{2}}}{4}\]

B)  \[\left( {{m}_{1}}+{{m}_{2}}+{{m}_{3}} \right){{a}^{2}}\]

C)  \[\left( {{m}_{1}}+{{m}_{2}} \right)\frac{{{a}^{2}}}{4}\]

D)  \[\left( {{m}_{2}}+{{m}_{3}} \right){{a}^{2}}\]

E)  None of the above

Correct Answer: A

Solution :

                Moment of inertia of system about the axis which passing through\[{{m}_{1}}\] \[{{I}_{system}}={{m}_{1}}{{(0)}^{2}}+{{m}_{2}}{{\left( \frac{a}{2} \right)}^{2}}+{{m}_{3}}{{\left( \frac{a}{2} \right)}^{2}}\] \[{{I}_{system}}=({{m}_{1}}+{{m}_{3}})\frac{{{a}^{2}}}{4}\]