The pressure that has to be applied to the ends of a steel wire of length 10cm to keep its length constant when its temperature is raised by 100∘C is:- Given: Y=2×1011N/m2 and α=1.1×10−5/∘C
A
2.2×108Pa
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B
2.2×109Pa
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C
2.2×107Pa
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D
2.2×106Pa
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Solution
The correct option is A2.2×108Pa 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=2×1011N/m2α=1.1×10−5/∘CΔT=100∘C, ⎤⎥
⎥⎦ we get, P=2×1011×1.1×10−5×100 ⇒P=2.2×108N/m2 ∴P=2.2×108Pa This is the required pressure that has to be applied to keep the length of the rod constant.