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Question

At 0C, a square steel bar of 1cm side, is rigidly clamped at both ends so that its length cannot increase. Young's modulus of steel is 20×1010Nm2 and its coefficient of linear expansion is 11×106/C. When the temperature is raised to 10C , the force exerted on the clamp is

A
1100N
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B
2200N
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C
3300N
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D
4400N
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Solution

The correct option is B 2200N
Length, l=1cm=0.01m
Change in temperature =dt=10 [change in temperature in degree kelvin is same as degree centigrade]
Y=stress/strain
=(F/A)/dl/l
Now, α=dl/(ldt)
or, dl=lαdt
Putting the value of dl we get,
Y=F/(αdtA)
Or, F=YαdtA
Putting value of α=11 X 106, Y=20 X 1010, dt = 10 and A = (0.01)2
We get force as 22×102 N

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