Question

What would be the change in escape velocity, if the radius of the Earth reduces 4% and mass remains constant?

Answer 1

Escape velocity,
v_e = \(\sqrt{\frac{2 G M}{R}}=\sqrt{2 G M} R^{-\frac{1}{2}}\)
From this formula, it is clear that on decreasing the value of R_e escape velocity v_e will increase.
∴ For maximum percentage error in v_e

∴ Percentage increase in escape velocity = 2%