Question

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 in temperature of the steel rod when heated is
`(Y = 3 xx 10^(11)N // m^(2) , alpha = 1.1 xx 10^(-5 //@)C)`
A. `20^(@)`C
B. `15^(@)`C
C. `10^(@)`C
D. `0^(@)`C

Answer 1

c) Modulus of elasticity = (Force/Area) `xx(l)/(Deltal)`
`3 xx 10^(11) = (33000)/(10^(-3)) xx l/(Deltal)`
`(Deltal)/l = (33000)/(10^(-3)) xx 1/(3 xx 10^(11)) = 11 xx 10^(-5)`
Charge in length, `(Deltal)/(l) = alphaDeltaT`
`11 xx 10^(-5) = 1.1 xx 10^(-5) xx DeltaT rArr DeltaT = 10K` or `10^(@)`C