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 therma expansion is `1.1 xx 10^(-5)K^(-1)`)

Options

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

Answer

B

Explanation

Given, `Delta =100^(@)C, Y =2xx10^(11) Nm^(-2)`
`alpha =1.1xx10^(-5)K^(-1)`
Thermal strain in the wire `= alpha Delta T`
[As `l=l_(0) (1+alpha Delta T)`]
Thermal stress in rod is the pressure due to the thermal strain.
Required pressure `= Y alpha Delta T =2xx10^(11) xx1.1xx10^(-5)xx100=2.2xx10^(8) Pa`