First slide

Variation of g

Question

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

Moderate

A

Decrease by 2%
B

Remain unchanged
C

Increase by 2%
D

Increase by 1%

Solution

$g = \frac{GM}{R^{2}} .$ If mass remains constant then $g \propto \frac{1}{R^{2}}$
% increase in g = 2(% decrease in R) =2 × 1% = 2%

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