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 mass of earth and angular momentum constant, then

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g increases by 2 % and K increases by 2%

g increases by 4 % and K increases by 4%

g decreases by 4 % and K decreases by 2%

g decreases by 2 % and K decreases by 4%

answer is B.

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Detailed Solution

g=GMR2g∝R-2change in g=(-2)(% change in R)=(-2)(-2)=+4%Rotational kinetic energy,K=L22IL= angular momentum = constant I=25mR2K∝R-2% change in K=(-2)(% change in R)=(-2)(-2)=+4%

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