JEE Main 2019 — Physics solution

JEE Main2019Physics

A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to:

A
9F / ( $π$ r²YT)
B
3F / ( $π$ r²YT)
C
F / (3 $π$ r²YT)
D
6F / ( $π$ r²YT)

Solution

$Y = \frac{FL}{A∣ΔL∣} \Rightarrow ΔL = \frac{FL}{AY} = L α T$

$α = \frac{F}{AYT}$

$γ = 3 α = \frac{3F}{π r ^{2} YT}$

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