When the earth shrinks its radius decreases, at the same time density increases. Expression for acceleration due to gravity can be written as g = G(4/3)3.14 Rd. Then how the value of 'g' increases. It should remain the same. Is this correct?
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Answer: No, the 'g' will increase as the earth shrinks without change in the mass
Explanation:
Let us see the same situation in a different point of view
g = GM/R^2
From the formula we can see g is inversely proportional to square of the radius R^2
As 'R' decreases 'g' will increase.
Coming to your fórmula, which is correct,
The point here is that density 'd' increases more rapidly than the decrease in radius that's why 'g' increases.
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