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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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Knowledge Check

  • The strain energy per unit volume of a stretched wire is

    A
    `1//2 xx ` stress `xx` strain
    B
    `1//2 xx ("strain")^(2)xx Y`
    C
    `1//2 xx ("stress")^(2)//Y`
    D
    all of these

  • Two wires of the same material and same mass are stretched by the same force. Their lengths are in the ratio

    A
    `3:2`
    B
    `2:3`
    C
    `4:9`
    D
    `9:4`

  • Energy per unit volume in a stretched wire is

    A
    Half of load `xx` strain
    B
    Load `xx` strain
    C
    Stress `xx` strain
    D
    Half of stress `xx` strain

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