Chapter 13, Problem 88GP

To determine

To Find: The height above the earth.

Answer to Problem 88GP

The height above the earth at which steel band would be $1531\text{ m}$ .

Explanation of Solution

Given info:

Initial temperature, $T_1={25}^{\circ }\text{C}$ .

Final temperature, $T_2=45{}^{\circ }\text{C}$ .

Radius of earth, $r=6.38\times {10}^6\text{ m}$ .

Initial length, $l_0=2\times \pi \times r$ .

Formula used:

Write the expression for change in length.

  $\Delta l=l_0\times \alpha \times \Delta T$

Here, $l_0$ is the initial length,

  $\Delta T$ is the change in temperature,

  $\alpha$ is the coefficient of expansion.

Calculation:

Substitute the given values in the above equation,

  $\begin{array}{l}2\times \pi \times \Delta r=2\pi r\times 12\times {10}^{-6}\times 20\\ \Delta r=6.38\times {10}^6\times 12\times {10}^{-6}\times 20\\ \Delta r=1531\text{ m}\end{array}$

Conclusion:

Thus, the height above the earth at which steel band would be $1531\text{ m}$ .