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

Answer

A

Explanation

(a) Young's modulus Y=stress/strain
`stress=Yxxstrain`
Stress in steel wire =Applied pressure
`Pressure=stress=Yxxstrain`
`Strain=(DeltaL)/L= alphaDeltaT` (As length is constant)
`=2xx10^11xx1.1xx10^-5xx100`
`=2.2xx10^8Pa`