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Calculate the compressional force requir...

Calculate the compressional force required to prevent the metallic rod length `l cm` and cross-sectional area `A cm^(2)` when heated through `t^(@)C`, from expanding along length wise. The Young's modulus of elasticity of the metal is `E` and mean coefficient of linear expansion is `alpha` per degree Celsius

A

`E A alpha t`

B

`(EA alphat)/((1+alphat))`

C

`(EA alphat)/((1-alphat))`

D

`El alphat`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Calculate the compressional force required to prevent the metallic rod of length l cm and cross sectional area Acm^2 when heated through t^@C from expanding lengthwise. Young's modulus of elasticity of the metal is E and mean coefficient of linear expansion is alpha per degree celsius.

    A
    `EA alpha t`
    B
    `E A alpha t//((1+alpha t)`
    C
    `E A alpha t//(1- a t)`
    D
    `E l alpha t`

  • The increase in energy of a metal bar of length L and cross-sectional area A when compressed with a load M along its length is (where, Y= Young's modulus of the material of metal bar)

    A
    `(FL)/(2AY)`
    B
    `(F^(2)L)/(2AY)`
    C
    `(FL)/(AY)`
    D
    `(F^(2)L^(2))/(2AY)`

  • A metal rod of length 'L' and cross-sectional area 'A' is heated through 'T'^(@)C What is the force required to prevent the expansion of the rod lengthwise ?

    A
    `(YAalphaT)/((1-alphaT)`
    B
    `(YAalphaT)/((1+alphaT))`
    C
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    D
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