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A uniform metal rod of 2mm^(2) area of c...

A uniform metal rod of `2mm^(2)` area of cross section is heated from `0^(@)C` to `20^(@)C`. The coefficient of linear expansion of the rod is `12xx10^(-6)//""^(@)C`. Its Young's modulus of elasticity is `10^(11)N//m^(2)`, then the energy stored per unit volume of rod is,

A

`1440 J//m^(3)`

B

`2880 J//m^(3)`

C

`1200 J//m^(3)`

D

`3880J//m^(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
`u=(1)/(2)(F)/(A) xx (l)/(L) =(1)/(2)(F)/(A) xx prop Delta t`
But `Y=(F)/(A) (l)/(L) " " therefore F=(Yal)/(L)`
`u=(1)/(2)Y(alpha Delta t)^(2)`
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Knowledge Check

  • A uniform metal rod fixed at its ends of 2 mm^(2) cross-section is cooled from 40@^C to 20^@C . The coefficient of the linear expansion of the rod is 12xx10^(-6) per degree celsius and its young's modulus of elasticity is 10^11 N//m^(2). The energy stored per unit volume of the rod is

    A
    `2880 J//m^(3)`
    B
    `1500 J//m^(3)`
    C
    `5760 J//m^(3)`
    D
    `1440 J//m^(3)`

  • A uniform rod of cross-section 4 mm^(2) is heated from 0^(@)C " to "10^(@)C. The coefficient of linear expansion of the rod, prop=12xx10^(-6)//^(@)C and Young's modulus =10^(11)N//m^(2). The strain produced in the rod is

    A
    `8xx10^(-4)`
    B
    `12xx10^(-4)`
    C
    `8xx10^(-5)`
    D
    `12xx10^(-5)`

  • The coefficient of linear expansion of a metal rod is 12 xx 10^(-6//0)C , its value in per ^(0)F

    A
    `(20)/(3) xx 10^(-6//0)F`
    B
    `(15)/(4) xx 10^(-6//0)F`
    C
    `21.6 xx 10^(-6//0)F`
    D
    `12 xx 10^(-6//0)F`

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