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Question

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100C is:-
Given: Y=2×1011 N/m2 and α=1.1×105 /C

A
2.2×108 Pa
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B
2.2×109 Pa
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C
2.2×107 Pa
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D
2.2×106 Pa
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Solution

The correct option is A 2.2×108 Pa
When temperature is increased, length of the rod also increases. To keep the rod at constant length, we have to apply pressure at the ends to oppose expansion.
Let the pressure applied be P.


We know, Young's modulus Y=stressstrain=PΔLL=PLΔL
[stress=FA=P]
Y=PLΔL
P=YΔLL
[From thermal expansion, the change in length, ΔL=LαΔT]
P=Y(LαΔT)L
P=YαΔT

Substituting the values,
⎢ ⎢Y=2×1011 N/m2α=1.1×105/CΔT=100C, ⎥ ⎥
we get, P=2×1011×1.1×105×100
P=2.2×108 N/m2
P=2.2×108 Pa
This is the required pressure that has to be applied to keep the length of the rod constant.

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