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The acceleration due to gravity (g) on the surface of earth is $g = \frac{GM}{R^{2}},$ where M is mass of earth, R is radius of earth and G is universal gravitational constant. If mass of earth decreases by 2% and radius decreases by 1%, then percentage change in value of g is

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4% decrease

2% decrease

4% increase

Zero

answer is A.

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Detailed Solution

$g = \frac{GM}{R^{2}}$

$\Rightarrow \frac{Δg}{g} \times 100 = \frac{ΔM}{M} \times 100$

$- 2 (\frac{ΔR}{R} \times 100)$

$= (- 2) - 2 (- 1) = 0$

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