Two wires having same length and material are stretched by same force. Their diameters are in the ratio 1:3. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched is

Options

A. `3:1`
B. `9:1`
C. `27:1`
D. `81:1`

Answer

B

Explanation

According to question, energy in string per unit volume is given by `1/2xx "stress "xx "strain"`
i.e `U/V=1/2xxF/Axx(Deltal)/l` [Symbols have their usual meanings]
= `1/2xxVxx (strain)^2`
`therefore U_S/S_L=Y_S/Y_Lxx((stress(S))/(strain(L)))^2`
= `A_L/A_S=(l/l)^2`
`Rightarrow r_L^2/r_S^=3^2/1^2=9:1`