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
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
$g$ 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 $4\%$
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
$g = \frac{{GM}}{{{R^2}}}$ and $K = \frac{{{L^2}}}{{2I}}$
If mass of the earth and its angular momentum remains constant then $g \propto \frac{1}{{{R^2}}}$ and $K \propto \frac{1}{{{R^2}}}$
i.e. if radius of earth decreases by $2\%$ then $g$ and $K$ both increases by $4\%.$
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