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A body weighs 700 g-wt on the surface of the Earth. How much will it weigh on the surface of a planet whose mass is \(\frac{1}{7}\) of Earth’s mass and radius is half that of the Earth?

1. 200 g-wt
2. 400 g-wt
3. 50 g-wt
4. 300 g-wt

Correct answer: 400 g-wt

Solution

Weight is proportional to gravitational acceleration, and \(g\propto \frac{M}{R^2}\). Here the planet has mass \(\frac{1}{7}M_E\) and radius \(\frac{1}{2}R_E\), so \(g' = \frac{1/7}{(1/2)^2}g = \frac{4}{7}g\). Thus the new weight is \(700\times \frac{4}{7}=400\) g-wt.

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