1. The problem statement, all variables and given/known data Let g be the acceleration due to gravity at the 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 constant, (a) g increases by 2% and K increases by 2% (b) g increases by 4% and K increases by 4% (c) g decreases by 4% and K decreases by 2% (d) g decreases by 2% and K decreases by 4% 2. Relevant equations g=GM/R2 , where M & R is the mass and the radius of the Earth respectively K=(1/2)Iω2 , where I is the moment of inertia of the Earth about its axis of rotation and ω is it's angular velocity about the same axis 3. The attempt at a solution (dR/R)100 = 2% ..........(decrease) Since all other quantities are constant, i) g=GM/R2 ⇔ g ∝ R-2 ⇒ dg/g = 2(dR/R) ⇒ (dg/g)100 = 2((dR/R)100) = 2(2) = 4% .............(increase) Since there is inverse proportionality, g increases by 4% ii) K=(1/2)Iω2 Now, assuming the Earth to be a homogeneous sphere of uniform mass density, its moment of inertia about the diameter is I=(2/5)MR2 Therefore K= (1/2)(2/5)MR2ω2 = (1/5)MR2ω2 Keeping all other quantities constant, K ∝ R2 ⇒dK/K = 2(dR/R) ⇒(dK/K)100 = 2((dR/R)100) = 2(2) = 4% ................. (decrease) Since there is direct proportionality, K decreases by 4% Hence, g increases by 4% and K decreases by 4% So, I think option (b) should've been - g increases by 4% and K decreases by 4%, instead of K increases by 4% Thoughts?