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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 4 % and K increases by 4%

g decreases by 2 % and K decreases by 4%

g decreases by 4 % and K decreases by 2%

g increases by 2 % and K increases by 2%

answer is B.

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Detailed Solution

$g = \frac{G M}{R^{2}}$

$g \propto R^{- 2}$

change in $g = (- 2) (% change in R)$

=(-2)(-2)=+4%

Rotational kinetic energy,

$K = \frac{L^{2}}{2 I}$

$L = angular momentum = constant$

$I = \frac{2}{5} m R^{2}$

$K \propto R^{- 2}$

$% change in K = (- 2) (% change in R)$

$= (- 2) (- 2) = + 4 %$

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