a
moment of inertia is the product of mass and square of separation between particle and axis of rotation.

e.g. \(M . I=m r^{2}\)

here, we see, separation of mass \(\mathrm{m} 1\) and altitude \(N N^{\prime} i s 0 .\)

alteration between mass \(m_{2}\) and \(N N^{\prime}\) is \(\left(\frac{a}{2}\right)\) also for \(m_{3}\) separation is \(\left(\frac{a}{2}\right)\)

moment of inertia about altitude passing through \(m_{1}=I_{1}+I_{2}+I_{3}\)

where \(I_{1}, I_{2},\) and \(I_{3}\) are \(M . I o f m_{1}, m_{2}\) and \(m_{3}\) respectively.

\(M . I=m_{1} \cdot(0)+m_{2}\left(\frac{a}{2}\right)^{2}+m_{3}\left(\frac{a}{2}\right)^{2}\)

\(=\frac{a^{2}}{4 \times\left(m_{2}+m_{3}\right)}\)