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Question

A compressive force, F is applied at the two ends of a long thin steel rod. It is hated, simultaneously, such that its temperature increases by T . The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young,s modulus, and α its coefficient of linear expansion. Then, F is equal to :

A
l2YαT
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B
lAYαT
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C
AYαT
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D
AYαT
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Solution

The correct option is D AYαT
ΔLL=αΔT

StressStrain=Y

FAαΔT=Y

FA=YαΔT

F=AYαΔT

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