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Two wires having same length and materia...

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

A

`3:1`

B

`9:1`

C

`27:1`

D

`81:1`

Text Solution

Verified by Experts

The correct Answer is:
D
`L_(1)=L_(2),y_(1)=y_(2),f_(1)=f_(2),(d_(1))/(d_(2))=(1)/(2),(u_(1))/(u_(2))=?`
`(u_(1))/(u_(2))=(1)/(2)("stress")/(y)=(F^(2))/(d_(1)^(4))xx(d_(2)^(4))/(F_(1)^(2))=((d_(2))/(d_(1)))=(81)/(1)`
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