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

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g decreases by 2% and K decreases by 4%

g decreases by 4% and K increases by 2%

g increases by 4% and K increases by 4%

g decreases by 4% and K increases by 4%

answer is C.

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Detailed Solution

Radius is decreased by 2% i.e., -2% g=GMR2 g∝1R2 g∝R-2 g%=-2R%=-2(-2%)=+4% and K=L22I==L222MR25 K∝1R2 K∝R-2 K%=-2R%=-2(-2%)=+4%We are clearly given in the question that all the other quantities remain constant other than the radius of earth. So, we could conclude that earth’s mass and angular momentum remains constant.

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