The Young's modulus of material of wire 1 is twice that of wire 2 . When the wires 1 and 2 of same length are stretched by same force, they produce same extension. If R 1 and R 2 are the radii of wires 1 and 2 respectively, then

Step-by-step solution

Let us assume, Young modulus 1 be, Y 1 Young modulus 2 be, Y 2 Length of wire 1 be, L 1 Length of wire 2 be, L 2 Force on wire be, F Extension of both wire be δ 1 & δ 2 Given Young's modulus is, Y 1 = 2 Y 2 Length of both wire is same, L 1 = L 2 = L Radius of 1 be, R 1 Radius of 2 be, R 2 Forces on both are same. Extension of both wire be, δ 1 = δ 2 = δ From Hooke's law, we have F = A Y δ L For 1 , F = π R 1 2 Y 1 δ L 1 = π R 1 2 2 Y 2 δ L