Two wires of the same material (Young’s modulus Y) and same length L but radii R and 2R respectively are joined end to end and a weight w is suspended from the combination as shown in the figure. The elastic potential energy in the system is
K1=yπ(2R)2L
K2=yπ(R)2L
Equivalent 1K1+1K2=14yπ R2+Lyπ R2
Since,K1x1=K2x2=w
Elastic potential energy of the system
U=12k1x1+12k2x22
=12k1(Wk1)2+12k2(Wk2)2
=12W2+(1k1+1k2)
=12W2+(5L4yπ R2)
U=(5w2L8π yR2)