Question

The radius and mass of earth are increased by $0.5$%. Which of the following statements is false at the surface of the earth?

• A. $g$ will increase
• B. $g$ will not change
• C. Escape velocity will remain unchanged
• D. Potential energy will remain unchanged

Answer 1

Answer: (C), (D)

The correct options are
C Escape velocity will remain unchanged
D Potential energy will remain unchanged

$g=\frac{GM}{R^2},v_e=\sqrt{\frac{2GM}{R}}$ and $U=\frac{-GMm}{R}$
$\therefore g\propto \frac{M}{R^2},v_e\propto \sqrt{\frac{M}{R}}$ 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 $0.5\%$