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 decreases by 2 % keeping all other quantities same, then

Options

A. g decreases by 2% and K decreases by 4% .
B. g decreases by 4% and K decreases 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

`implies` According to equations `g = (GM)/r^2 and K=1/2 L^2/I`
`g prop 1/R^2 and K prop 1/R^2 " " ( :. I =2/5 MR^2)`