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 decreased 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%

Answer 1

Answer: (C)

$g=\frac{GM}{R^2}\Rightarrow \frac{\Delta g}{g}=-2\frac{\Delta R}{R}=-2(-2$
And $K=\frac{1}{2}I{\omega }^2=\frac{1}{2}{\omega }^2\times \frac{2}{5}M{R}^2$
$\frac{\Delta K}{K}=2\frac{\Delta R}{R}=2\times (-2)$