First slide

Variation of g

Question

If the radius of earth were to shrink by 1%, its mass remaining the same, the acceleration due to gravity on the earth's surface would :

Easy

A

increases by 1%
B

increases by 2%
C

decrease by 2%
D

decrease by 1%

Solution

$g = \frac{GM}{R^{2}} \Rightarrow g \propto R^{- 2} \Rightarrow \frac{Δg}{g} = - 2 \frac{ΔR}{R} = - 2 (- 1) = + 2 %$

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