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? [Y = Young's modulus of the material of rod, α = coefficient of linear expansion ]

Question

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? [Y = Young's modulus of the material of rod, α = coefficient of linear expansion ], Y A α T ( 1 - α T ), Y A α T ( 1 + α T ), ( 1 - α T ) Y A α T, ( 1 + α T ) Y A α T

MARKS App · Accepted Answer

∆ L = α L T ...... (i) Also Y = F A . L ( 1 + α t ) ∆ L Or ∆ L = F . L ( 1 + α t ) A . Y ........ (ii) Equating (i) and (ii) F . L 1 + α t A . Y = α L T ∴ F = A Y α T ( 1 + α t )

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