Let g be the acceleration due to gravity at the earth's surface and K the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2%. Keeping all other quantities constant, then

Options

A. `g` decreases by `2%` and `K` decreased by `4%`
B. `g` decreases by `4%` and `K` increased by `2%`
C. `g` increases by `4%` and `K` increased by `4%`
D. `g` decreases by `4%` and `K` increased by `4%`

Answer

C

Explanation

`g=(GM)/(R^(2))` and `K=(L^(2))/(2I)`
If mass of the earth its angular momentum remains constant then `g prop1/(R^(2))` and `K prop 1/(R^(2))`
i.e., if radius of earth decreases by `2%` then `g` and `K` both increases by `4%`.