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 con

Question

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

TestHub · Accepted Answer

g = G M R 2 % change in g = ( − 2 ) × (% change in R ) = ( − 2 ) ( − 2 ) = + 4 % Rotational kinetic energy K = L 2 2 I Angular momentum L is constant and I = 2 5 m R 2 K ∝ R − 2 % change in K = ( − 2 ) × (% change in R ) = ( − 2 ) ( − 2 ) = + 4 %

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