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 xx 10^(11) N//m^(2)` and the coefficient of linear expansion of steel is `1.1 xx 10^(-5)//^(@)C`)

Options

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

Answer

C

Explanation

Modulus of elasticity `=("Force")/("Area") xx (l)/(Delta l)`
`3xx10^(11)=(33000)/(10^(-3))xx(l)/(Delta l)`
`(Delta l)/(l) =(33000)/(10^(-3))xx(1)/(3xx10^(11))=11xx10^(-5)`
Change in length, `(Delta l)/(l) = alpha Delta T`
`11xx10^(-5) =1.1xx10^(-5) xx Delta T" or "Delta T =10 K" or "10^(@)C`