A metal rod of length ′ L ′ and cross-sectional area ′ A ′ is heated through ′ T ′ degree C . What is the force required to prevent the expansion of the rod lengthwise? [ Y = Young's modulus of the material of rod, α − coefficient of linear expansion]

Home » A metal rod of length ′ L ′ and cross-sectional area ′ A ′ is heated through ′ T ′ degree C . What is the force required to prevent the expansion of the rod lengthwise? [ Y = Young’s modulus of the material of rod, α − coefficient of linear expansion]

A metal rod of length ′ L ′ and cross-sectional area ′ A ′ is heated through ′ T ′ degree C . What is the force required to prevent the expansion of the rod lengthwise? [ Y = Young’s modulus of the material of rod, α − coefficient of linear expansion]

Physics | Physics

A metal rod of length ′ L ′ and cross-sectional area ′ A ′ is heated through ′ T ′ degree C . What is the force required to prevent the expansion of the rod lengthwise? [ Y = Young’s modulus of the material of rod, α − coefficient of linear expansion]

Solution: The correct answer is B.

$change\text{ }in\text{ }length:\,~\delta L=L\alpha T$

$final\text{ }length~\,{{L}_{f}}=L+\delta L$

Now, in order to limit the expansion, there must be a force that compresses the rod by $\delta L$

$strain=\frac{\delta L}{{{L}_{f}}}$

$Y=\frac{F/A}{strain}$

$F=\frac{YA\alpha T}{1+\alpha T}$

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