The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by `100^(@)C`is :
(For steel Young's modulus is `2 xx 10^(11)N m^(-2)` and coefficient of thermal expansion is`1.1 xx 10^(-5) K^(-1)`)

Options

A. `2.2 xx 10^(7) Pa`
B. `2.2 xx 10^(6) Pa`
C. `2.2 xx 10^(8) Pa`
D. `2.2 xx 10^(9) Pa`

Answer

C

Explanation

Thermal strain = `alpha DeltaT`
(by l = `l_(0)(1+alphaDeltaT)`)
`implies` Thermal stress in Rod
(Pressure due to Thermal strain)
=`Y alphaDeltaT`
=`2 xx 10^(11) xx 1.1 xx 10^(-5) xx 100`
= `2.2 xx 10^(8)Pa`