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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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 increases by 4%
d
g decreases by 4% and K increases by 4%
answer is C.
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Detailed Solution
g=GMR2 and K=L22IIf mass of the earth and its angular momentum remains constant then g∝1R2 and K∝1R2i.e. if radius of earth decreases by 2% then g and K both increases by 4%.