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# The length of a steel cylinder is kept constant by applying pressure at its two ends. When the temperature of rod is increased by 100oC from its initial temperature, the increase in pressure to be applied at its ends is

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a
22×107 atm
b
2.2×103atm
c
zero
d
4.3×103atm
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detailed solution

Correct option is B

If the rod is allowed to expand, then it will expand by Δl=lα ΔT due to increase in temperature by ΔT. But as the length of the cylinder is kept constant by applying pressure, a stress is developed in the cylinder. The decrease in length of cylinder due to elasticity is Δl=lαΔT and a compressive stress will develop in it.Stress = Excess pressure applied at ends∆P=Y×Δll=YαΔT=2×1011×11×10−6×100=2.2×103atm

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