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

Answer

C

Explanation

g = `(GM)/(R^(2)) = GMR^(-2)`,
`therefore (Delta g)/(g) xx 100 = - 2 (Delta R)/(R) xx 100 = -2 xx (-2 %)`
AlsoK = `(1)/(2) I omega^(2) , therefore (Delta K)/(K) = (Delta I)/(I)` ,
As I = `KR^(2), " so" (Delta I)/(I) = (2 Delta R)/(R)`
`therefore (DeltaK)/(K) xx 100 = 2 ((Delta R)/(R) xx 100) = 2 (-2%) = - 4% `.