Gravitation Question 331
Question: If the radius of the earth were to shrink by 1 %, with its mass remaining the same, the acceleration due to gravity on the earth’s surface would
Options:
A) Decrease by 1%
B) decrease by 2%
C) Increase by 1%
D) increase by 2%
Show Answer
Answer:
Correct Answer: D
Solution:
-
As $ [g=\frac{GM}{R^{2}}] $
when radius is reduced by 1% then $ [R’=R-\frac{R}{100}=.99R,] $
so $ [g’=\frac{GM}{{{(.99R)}^{2}}}=1.02\frac{GM}{R^{2}}] $
%$ [\Rightarrow increase=2] $ %
