Q. Let $g$ be the acceleration due to gravity at earth’s surface and $K$ be the rotational kinetic energy of the earth. Suppose the earth’s radius decreases by 2% keeping all other quantities same, then
A) $g$ decreases by 2% and $K$ decreases by 4%
B) $g$ decreases by 4% and $K$ increases by 2%
C) $g$ increases by 4% and $K$ increases by 4%
D) $g$ decreases by 4% and $K$ increases by 4%
Explanation
(c) $g = \frac{GM}{R^{2}}$ and $K = \frac{L^{2}}{2I}$
If mass of the earth and its angular momentum remains constant then $g \propto \frac{1}{R^{2}}$ and $K \propto \frac{1}{R^{2}}$
$i.e.,$ if radius of earth decreases by 2% then $g$ and $K$ both increases by 4%
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.