A steel wire of cross-sectional area `0.5mm^2` is held between two fixed supports. If the wire is just taut at `20^@C`, determine the tension when the temperature falls to `0^@C`. Coefficient of linear expansion of steel is `1.2 xx 10^(-5)C^(-1)` and its Young's modulus is `2.0 xx 10^11 N m^(-2).`

Options

A. `30^(@)C`
B. `55^(@)C`
C. `65^(@)C`
D. `70^(@)C`

Answer

D

Explanation

A steel ball ………..
`D_(s)-D_(H) = 0.05mm`
Where `D_(s)` is diameter of ball and `D_(H)` is diameter of ball hole. As we increase temperature
`D_(H)gtD_(s)` for ball to enter hole
`D_(H)(1+12xx10^(-6)DeltaDeltaT)-D_(s)(1+(3.2)/(3)xx10^(-6)Delta T)gt0`
`(12xx10^(-4)- (3.2)/(3)xx10^(-4))Delta Tgt0.05`
Given `Delta T gt 46^(@)`