2 Rods of length l and 2l , Area 2A and A are joined end to end . Now by hammering we change the area of rod from 2A to A . Find moment of inertia about the joint in final condition . It is given that both the rods have some density$\;\rho$

Question

$(a)\;\large\frac{10}{3} \rho A l^{3} \qquad(b)\;\large\frac{8}{3} \rho A l^{3}\qquad(c)\;\large\frac{4}{3} \rho A l^{3}\qquad(d)\;\large\frac{16}{3} \rho A l^{3}$