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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:
b
According to question, energy in string per unit volume is given by `(1)/(2) xx` stress `xx` strain
i.e., `(U)/(V) = (1)/(2) xx (F)/(A) xx (Delta l)/(l)`
[Symbols have their usual meanings]
`= (1)/(2) xx V xx ("strain")^(2)`
`:. (U_(s))/(S_(L)) = (Y_(s))/(Y_(L)) xx ("Stress"(S))/("Strain"(L))^(2)`
`= (A_(L))/(A_(S)) = ((l)/(l))^(2)`
`implies (r_(L)^(2))/(r_(s)^(2)) = (3^(2))/(1^(2)) = 9 : 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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