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Q.

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%.
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