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Question

A metal bar of length 1 m and area of cross-section 1 mm2 is clamped between two rigid supports. For the material of rod, its Young's modulus is Y=1011 N/m2 and coefficient of linear expansion is α=1.8×105 C1. If the temperature of the rod is decreased by ΔT=10C, the force exerted by the rod on the supports is

A
9 N
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B
6 N
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C
16 N
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D
18 N
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Solution

The correct option is D 18 N
We know,
Thermal stress =YαΔT
For cooling,
ΔT is negative.
We use |ΔT|.
Thermal stress =Yα|ΔT|
=1011×1.8×105×10
=1.8×107 N/m2

Also,
Force on the suppport,
F=YAα|ΔT|=A× stress
=1×106×1.8×107 N
F=18 N

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