First slide

Gravitational potential and potential energy

Question

The radius and mass of earth are increased by 0.5%. Which of the following statements are true at the surface of the earth

Moderate

A

g will increase
B

g will decrease
C

Escape velocity will remain unchanged
D

Potential energy will remain unchanged

Solution

$g = \frac{GM}{R^{2}}, v_{e} = \sqrt{\frac{2 GM}{R}} and U = \frac{- GMm}{R}$
$∴ g \propto \frac{M}{R^{2}}, v_{e} \propto \sqrt{\frac{M}{R}} and U \propto \frac{M}{R}$
If both mass and radius are increased by 0.5% then v_e and U remains unchanged where as g decrease by 0.5%.

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