A rod of length L is composed of a uniform length L/2 of wood whose mass is M_w and a uniform length L/2 of brass whose mass is M_b

The moment of inertia of rod about an axis passing through the centre and perpendicular to it is $\frac{1}{12}{\mathrm{M}}_{\mathrm{w}}{\mathrm{L}}^2$

 The moment of inertia of rod about an axis passing through the centre and perpendicular to it is  $\frac{1}{12}\left({\mathrm{M}}_{\mathrm{w}}+{\mathrm{M}}_{\mathrm{b}}\right){\mathrm{L}}^2$

The moment of inertia of rod about an axis passing through the free end of wood  and perpendicular to the rod is $\frac{1}{3}\left({\mathrm{M}}_{\mathrm{w}}+{\mathrm{M}}_{\mathrm{b}}\right){\mathrm{L}}^2$

The moment of inertia of rod about an axis passing through the free end of wood  and perpendicular to the rod is $\frac{1}{12}\left({\mathrm{M}}_{\mathrm{w}}+7{\mathrm{M}}_{\mathrm{b}}\right){\mathrm{L}}^2$.