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 wires when stretched will be of the ratio.

Options

A. `16:1`
B. `4:1`
C. `2:1`
D. `1:1`

Answer

A

Explanation

(a) `Deltal=(Fl)/(AY)implies(Deltal)/(l)=((F)/(AY))`
Potential energy per unit volume `=(1)/(2)xx"stress"xx"strain"`
`u=(1)/(2)xx(F)/(A)xx(F)/(AY)` or `u prop (1)/(A^(2))` or `u prop (1)/(d^(4))`
`therefore (u_(1))/(u_(2))=((d_(2))/(d_(1)))^(4)=(16)/(1)`