The moment of inertia of a body about an axis is equal to its moment of inertia about a parallel axis through its centre of gravity plus the product of the mass of the body and the square of the perpendicular distance between the two parallel axes.
Let 'I' be the moment of inertia of a plane lamina about an axis YY. Let 'G' be the centre of gravity of the lamina. Yl Yl is an axis parallel to YY and passing through 'G'. Let 'Ig' be the moment of inertia of the lamina about Yl Yl.
Let GP = x.
Moment of inertia of the particle about
Y Y = m (x + d)2
Moment of inertia of the whole of lamina about
The lamina will balance itself about its centre of gravity. So the algebraic sum of the moments of the weights of constituent particles about the centre of gravity G should be zero.
