Question

When the radius and mass of earth are increased by 0.5%. Which of the following statement is correct at the surface of the earth?

Moderate

Solution

As we know that, $g = \frac{G M}{R^{2}}, v_{e} = \sqrt{\frac{2 G M}{R}}$
and $U = \frac{- G M m}{R}$
$∴ g \propto \frac{M}{R^{2}}, v_{e} \propto \sqrt{\frac{M}{R}} and U \propto \frac{M}{R}$
If both mass and radius are increased by 0.5%, then escape velocity and potential energy remains unchanged, whereas g decreases by 0.5%.
Thus, option (a) is correct but rest are incorrect.

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