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

Answer

C

Explanation

Thermal strain in the wire,
`(Deltal)/(l)=alphaDeltaT`
Thermal stress in rod is the pressure due to the thermal strain ltbRgt 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)xx1.1xx1^(-5)xx100=2.2xx10^(8)Pa`