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

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Solution

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Acceleration due to gravity at a depth d from surface of earth

$$g' = g \left(1 - \dfrac{d}{R} \right) $$ ....(1)

Where g = acceleration due to gravity at earth's surface

Multiplying by mass 'm' on both sides of (1)

$$\implies mg' = mg \left(1 - \dfrac{d}{R} \right) \, \,\, \, Here, \left(d = \dfrac{R}{2} \right)$$

$$= 200 \left(1 - \dfrac{R}{2 R} \right) = \dfrac{200}{2} = 100 N$$

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