Gravitation Question 32
Question: 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 [BHU 1994; JIPMER 2000]
Options:
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%
Show Answer
Answer:
Correct Answer: C
Solution:
$ [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%.
