Kevin S. Huang

2010: Problem 21

Topic: Gravity
Concepts: Binding energy, Dimensional analysis

Solution:

Recall the binding energy of a solid sphere of mass $M$ and radius $R$ is

U_{\text{bind}}=\frac{3GM^2}{5R} \propto \frac{GM^2}{R}

We could also have obtained the scaling from dimensional analysis. We have

M \propto \rho R^3

U_{\text{bind}} \propto G\rho^2R^5

If the radius is doubled, the energy increases by a factor of $2^5=32$ so the answer is E.

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2010, F=ma Exam

Binding energy, Dimensional analysis, Fma: Gravity

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