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 : (For steel Young's modulus is `2xx10^11 Nm^-2` and coefficient of thermal expansion is `1.1xx10^-5K^_1`)

Options

A. `2.2xx10^(7)` Pa
B. `2.2xx10^(9)` Pa
C. `2.2xx10^(8)` Pa
D. `2.2xx10^(6)` Pa

Answer

C

Explanation

Thermal strain in the wire, `(Deltal)/(l)=alphaDeltaT`
Thermal stress in rod is the pressure due to the thermal strain
Thermal stress `=Yxx` strain `=Y((Deltal)/(l))`

Thermal stress `=(F)/(A)=` pressure `=YalphaDeltaT`
Given , `DeltaT=100^(@)C,Y=2xx10^(11)Nm^(-2)alpha=1.1xx10^(-5)K^(-1)`
Pressure `=2xx10^(11)xx1.1xx10^(-5)xx100=2.2xx10^(8)pa`