Q. 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 $m_{1}$ 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) $\left( m_{2} + m_{3} \right)a^{2}$
Explanation
(a) M.I. of system about the axis which passing through $m_{1}$
$I_{system} = m_{1}(0)^{2} + m_{2}\left( \frac{a}{2} \right)^{2} + m_{3}\left( \frac{a}{2} \right)^{2}$
$I_{system} = \left( m_{2} + m_{3} \right)\frac{a^{2}}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.