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. `22xx10^(7)atm`
B. `2.2xx10^(3)atm`
C. zero
D. `4.3xx10^(3)atm`

Answer

B

Explanation

If the rod is allowed to expand then it will expand by `/_\l=lalpha /_\T` due to increase in temperature by `/_\T`. But as the length of the cylinder is kept constant by applying pressure, a stress is developed in te cylinder. The decrease in length of cylinder due to elasticity is `/_\l=l alpha/_\T ` and a compressive stress will develop it.
Stress=Excess pressure applied at ends
`=Yxx(/_\l)/lYalpha/_\T`
`=2xx10^(11)xx11xx10^(-6)xx10=2.2xx10^(3)atm`