A copper collar is to fit tightly about a steel shaft that has a diameter of 6 cm at `20^@C`. The inside diameter of the copper collar at the temperature is `5.98cm`
Q. To what temperature must the copper collar be raised to that it will just slip on the steel shaft, assuming the steel shaft remains at `20^@C` ? `(alpha_("copper")=17xx10^(-6)//K`)

Options

A. `324^@C`
B. `21.7^@C`
C. `217^@C`
D. `32.4^@C`

Answer

C

Explanation

`l_1=l_0(1+alphat)`
`(2pixx6)/(2)=l_0(1+alphat)`
`(2pixx5.98)/(2)=l_0(1+20alpha)`
`(6)/(5.98)=(1+alphat)/(1+20alpha)=((1+17xx10^-6t))/(1+20xx17xx10^-6)`
`t=216.8^@Capprox217^@C`