Two wires of the same material and length but diameters in the ratio 1 : 2 are stretched by the same force. The potential energy per unit volume for the two wire when stretched will be in the ratio

Options

A. 1:4
B. 4:1
C. 16 : 1
D. 1 : 16

Answer

D

Explanation

`U=(1)/(2)(AY)/(L)(Delta L)^(2)`
`(U)/(2L)=u=(1)/(2)Y((DeltaL)/(L))^(2)`
`(u_(1))/(U_(2))[((DeltaL)_(1))/((Delta L)_(2))]^(2)=((A_(2))/(A_(1))^(2))=[((pi)/(4)(d)^(2))/((pi)/(4)(2d)^(2))]^(2) =(1)/(16)`