First slide

Variation of g

Question

A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth?

Easy

A

100 N
B

150 N
C

200 N
D

250 N

Solution

$Acceleration due to gravity at a depth d, g_{d} = g (1 - \frac{d}{R}) For d = R / 2 \Rightarrow g_{d} = g (1 - \frac{R / 2}{R}) = \frac{g}{2} Required weight W^{'} = {mg}_{d} = \frac{mg}{2} = \frac{W}{2} = \frac{200}{2} = 100 N$

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