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A metallic rod l cm long, A square cm in...

A metallic rod l cm long, A square cm in cross-section is heated through `t^(@)"C"`. If Young’s modulus of elasticity of the metal is E and the mean coefficient of linear expansion is `alpha` per degree celsius, then the compressional force required to prevent the rod from expanding along its length is

A

`EA alphat`

B

`EA alphat//(1+alphat)`

C

`EA alpha t//(1-alpha t)`

D

`E l alpha t`

Text Solution

Verified by Experts

The correct Answer is:
A
`E=(F//A)/(Delta l//l)=("stress")/("strain")` where `Delta l=(l.-l)=l alphat " so " F=EA alpha t`
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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`

  • Calculate the compressional force required to prevent the metallic rod of length l cm and cross - sectional area A cm^(2) when heated through t^(@)C , from expanding lengthwise. Youngs 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
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  • 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 Celsiuss

    A
    `EAalphat`
    B
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    C
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    D
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