Question

A steel tape is placed around the earth at the equator when the temperature is ${10}^{\circ }C$. What will be the clearance between the tape and the ground (assumed to be uniform ) if the temperature of the tape rises to ${40}^{\circ }C$? Neglect expansion of the earth. Radius of earth at equator is $6400km$ & $\alpha =1.2\times {10}^{-5}{K}^{-1}$.

• A. 2.3 m
• B. 2.1 m
• C. 2.3 km
• D. 230 m

Answer 1

The correct option is C 2.3 km

This is a case of radial expansion, which is similar to linear expansion

Initial radius of steel ring $=6400km$ (radius of earth)

$=R_0=6.4\times {10}^{6}m$

and temperature rise, $\Delta T=({40}^{o}C-{10}^{o}C)=30K$

so expansion would be after thermal expansion

$\frac{\Delta R}{R_0}=\propto \Delta T$

$=\Delta R=R_0\propto \Delta T$

$=\Delta R=6.4\times {10}^6\times 1.2\times {10}^{-5}\times 30$

$=2.3\times {10}^{3}m$

$=2.3km$