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 ?

Answer 1

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)
$$\implies mg' = mg \left(1 - \dfrac{d}{R} \right) \, \,\, \, Here, \left(d = \dfrac{R}{2} \right)$$
$$= 200 \left(1 - \dfrac{R}{2 R} \right) = \dfrac{200}{2} = 100 N$$