Chapter 1, Problem 48GP

To determine

To Estimate: The diameter of the oil stick.

Answer to Problem 48GP

  $d=3\times {10}^3\text{ m}$

Explanation of Solution

Given:

Volume of oil, $V=1\times {10}^3\text{ cm}$

Diameter of oil molecules = thickness of oil slick, $t=2\times {10}^{-10}\text{ m}$

Formula used:

Volume of oil = area $\times$ thickness

Calculation:

  $\begin{array}{l}V=\pi {\left(\frac{d}{2}\right)}^{2}t\\ d=2\sqrt{\frac{V}{\pi t}}\\ d=2\sqrt{\frac{1000{\text{ cm}}^3{\left(\frac{1\text{ m}}{100\text{ cm}}\right)}^3}{\pi \times 2\times {10}^{-10}}}\\ d=3\times {10}^3\text{ m}\end{array}$

Conclusion:

  $d=3\times {10}^3\text{ m}$is the diameter of the oil slick.