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. `2.2 xx 10^6 pa`
B. `2.2 xx 10^8 Pa`
C. `2.2 xx 10^9 Pa `
D. `2.2 xx 10^7 Pa `

Answer

B

Explanation

At a particular temperature, length is constant,
`Y = ("Stress")/("strain") = (F/A)/((DeltaL)/(L) ) = ("Pressure ")/("strain")`
Also, Strain ` = (Delta L)/(L) = alpha Delta T`
` therefore ` Pressure = stress = Y x strain
` = 2 xx 10^11 xx 1.1 xx 10^(-5) xx 100`
` = 2.2 xx 10^8 Pa`