If the radius of the earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would

Question

Dr. Abubacker · Accepted Answer

(c) $g = \frac{GM}{R^{2}}$; If $R$ decreases then $g$ increases. Taking logarithm of both the sides;
$\log g = \log{G + \log{M = - 2\log R}}$
Differentiating it we get; $\frac{dg}{g} = 0 + 0 - \frac{2dR}{R}$
$= - 2\left( \frac{- 2}{100} ight) = \frac{4}{100}$
$	herefore\%$ increase in $g = \frac{dg}{g} 	imes 100 = \frac{4}{100} 	imes 100 = 4\%$

Q. If the radius of the earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would

Explanation

Reviewed by Dr. Abubacker

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