question_answer

Three point masses, each of mass m are placed at the corners of an equilateral triangle of side The moment of inertia of this system about, an axis along one side of the triangle is

A)  \[3\,m{{a}^{2}}\]                            

B)  \[2\,m{{a}^{2}}\]

C)  \[\frac{3}{4}m{{a}^{2}}\]            

D)        \[\frac{3}{2}m{{a}^{2}}\]

Correct Answer: C

Solution :

Moment of inertia of system about side AB is \[I=m{{(0)}^{2}}+m{{(0)}^{2}}+m{{\left( \frac{\sqrt{3}}{2}a \right)}^{2}}\] \[=\frac{3}{4}m{{a}^{2}}\]