Question

A body weighs 200 N on tge earth. how much will it weigh half way down to the centre?​

Answer 1

it will be the same as there is no change in weight of the object up or down to the earth

Answer 2

Answer:

The weight of the body half way down to the center will be 800 N.

Explanation:

Given that,

Weight of body = 200 N

Distance $d = \dfrac{R}{2}$

We know that,

Weight W = mg

$200=m\times9.8$

$m = \dfrac{200}{9.8}$

$m = 20.41\ kg$

We know that.

The gravity at the surface of the earth,

$g = \dfrac{GM}{R^2}$....(I)

The gravity at d distance below the surface of the earth,

$g' = \dfrac{GM}{(R-d)^2}$....(II)

Put the value of d in equation (II)

$g' = \dfrac{GM}{(R-\dfrac{R}{2})^2}$

$g'=\dfrac{GM}{R^2(1-\dfrac{1}{2})^2}$

$g'=\dfrac{GM}{R^2(\dfrac{1}{4})}$

g'=4g

The weight half way down to the center will be

$W'=mg$

$W' = 20.41\times4\times 9.8$

$W'=800\ N$

Hence, The weight of the body half way down to the center will be 800 N.