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

Energy denisty `=1/2xx"Stress"xx"Strain"`
`=1/2xx"Stress"xx"Stress"/Y=((Stress)^2)/(2Y)prop1/(D^(4))`
Now, `(u_(A))/(u_(B))=(D_(B)^(4))/(D_(A)^(4))=[2]^(4)=16`