Question

The radius and mass of earth are increased by 0.5%.Which of the following are true at the surface of earth? g will decrease Escape velocity will remain unchanged Potential energy will remain unchanged g will increase

• A. 1, 2 and 3 are correct.
• B. 1 and 2 are correct.
• C. 2 and 4 are correct.
• D. 1 and 3 are correct.

Answer 1

Answer: (A)

$g=\frac{GM}{R^2}$ $v_e=\sqrt{\frac{2GM}{R}}$ and $u=-\frac{G{M}_m}{R}$
$\therefore$ $g\propto \frac{M}{R^2},v_e\propto \sqrt{\frac{M}{R}}$ and $U\propto \frac{M}{R}$
If both mass and radius are increased by 0.5% then Vg and 7 remains unchanged whereas g decrease by 0.5%.