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 decreases by 4%
B. g decreases by 4% and K decreases by 2%
C. g decreases by 4% and K decreases by 4%
D. g decreases by 4% and K increases by 4%

Answer

B

Explanation

`K = (1//2) Iomega^(2) = (1//2) (2//5) MR^(2)omega^(2)`,
`g = GM//R^(2)`
`log g = log G + log M - 2 log R, (dg//g ) xx 100 = -2 (dR//R) xx 100 = -2 xx 2% =-4%`