Consider two wires of the same material and the same length stretched by the same force. If the ratio of diameters of these wires is `2 : 1`, then find the ratio of potential energy per unit volume of the second wire to that of the first wire:

Answer

`16.00`

Explanation

Potential energy per unit volume of the wire is:
`u = 1/2 xx ("Stress")^(2)/("Young.s modulus") = 1/2 S^(2)/Y`
Also, Stress `S = ("Force")/("Area")`
Given: `F_(1) = F_(2)`
`therefore S_(1)/S_(2) = A_(2)/A_(1)`
In this case: `Y_(1) = Y_(2)`
`therefore mu_(1)/mu_(2) = (S_(1)/S_(2))^(2) = (A_(2)/A_(1))^(2) = [(d_(2)/d_(1))^(2)]^(2) = 1/16`
`therefore mu_(2) = 16 mu_(1)`