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Question

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

A
$$200 N$$
B
$$250 N$$
C
$$150 N$$
D
$$100 N$$
Solution
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#### Correct option is D. $$100 N$$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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