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Question

If radius of the earth were to shrink by 1%, its mass remaining the same, g would decrease by nearly__________.

A
1%
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B
2%
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C
3%
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D
4%
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Solution

The correct option is A 2%
If mass of the planet remains the same then we can say that
gsurfaceα1r2
taking log both the sides we get
ln(g) = ln(k)- 2ln(r)
differentiating both sides we get
δgg=2δrr

if δrr = 1 %
then |δgg| = 2 %

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