show that moment of inertia of a thin uniform rod about an axis passing through a point midway between the centre and edge perpendicular to its length is 7ML²/48

Question

show that moment of inertia of a thin uniform rod about an axis
passing through a point midway between the centre and edge
perpendicular to its length is 7ML2/48

Vijaya Nittala · Accepted Answer

Using parallel axis theorem
I = ICM+Mx2(x is the distance of axis of rotation from centre of mass)As axis of rotation passes from L4(Midway between edge and centre of rod)So x= L2-L4=L4We know moment of inertia about centre of mass for  rod is ICM = ML212So I = ML212+ML42=7ML248

show that moment of inertia of a thin uniform rod about an axis passing through a point midway between the centre and edge perpendicular to its length is 7ML2/48

show that moment of inertia of a thin uniform rod about an axis passing through a point midway between the centre and edge perpendicular to its length is 7ML²/48