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Q.

Calculate the compressional force required to prevent the metallic rod of length l cm and cross-sectional area A cm2 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 a per degree Celsius

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a

EAαt

b

EAαt1+αt

c

EAαt1−αt

d

Elαt

answer is B.

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Detailed Solution

Natural length of the rod at t°C = l + lαtdecrease in natural length due to stress = ∆lΔ1−Δ=0;E=−F(l+Δ)AΔ;F=−EAat1+at
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Calculate the compressional force required to prevent the metallic rod of length l cm and cross-sectional area A cm2 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 a per degree Celsius