There is some change in length when a 33000 N tensile force is applied on a steel rod of area of cross-section `10^-3 m^2`. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is `3 xx10^11 N m^-2` and the coefficient of linear expansion of steel is `1.1 xx10^-5//^@c`)

Options

A. `20^@C`
B. `15^@C`
C. `10^@C`
D. `0^@C`

Answer

C

Explanation

Young's Modulus, `E=(Stress)/(strai n) =((fo rce)/(area))/((Deltal)/l)`
`3xx10^(11)=(330000/10^(-3))/((Deltal)/l)`
`therefore (Deltal)/l = 33000/10^(-3) xx 1/(3xx10^(11)) = 11xx10^(-5)`
Strain, `(Deltal)/l = propto DeltaT`
`11xx10^(-5)=1.1xx10^(-5)xxDeltaT`
`therefore DeltaT=10^@C`