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

Answer

C

Explanation

As `g=(GM)/(R^2)` and `k=(L^2)/(2I)=(L^2)/(2xx2/5MR^2)`
`Iprop1/(R^2)` and `Kprop1/(R^2)`
`therefore` both increases by 4%.