Question

Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. If the earth's radius decreases by 2% and keeping mass and angular momentum of earth to be constant, which one of the following is correct

• A. g increases by 2%, K increases by 2%
• B. g increases by 4%, K increases by 4%
• C. g increases by 4%, K increases by 2%
• D. g increases by 2%, K increases by 4%

Answer 1

The correct option is B g increases by 4%, K increases by 4%

We Know that $\begin{array}{cc}g=& \frac{GM}{R^2}\text{and}K=\frac{L^2}{2I}\end{array}$.

If mass of the earth and its angular momentum are remaining constant then we can say that
$\begin{array}{cc}g\propto & \frac{1}{R^2}\text{and}K\propto \frac{1}{R^2}\end{array}$

i.e. if radius of earth decreases by 2 % then $g$ and $K$ both increases by 4 %.