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 ?

CONCEPT:

The weight of the given body is the product of mass and acceleration due to gravity, it is written as;

F = mg

Here we are having m as the mass and g is the acceleration due to gravity.

and variation of the acceleration due to gravity down to the center of the earth is written as;

\(g = g\left( {1 - \frac{d}{R}} \right) \)

where g is the acceleration due to gravity, d is the depth of the surface and R is the radius.

CALCULATION:

Given: F = 200 N

The body will be halfway down to the center of the earth as shown in the figure below;

Now, the acceleration due to gravity at a depth d from the surface of the earth is 

\(g' = g\left( {1 - \frac{d}{R}} \right) \) ----(1)

When the body will halfway down to the center of the earth the acceleration due to gravity is written as;

\(d = \frac{R}{2}\)

⇒ \(g'=g(1-\frac{R}{2R})\) = g/2   ----(2)

∵ acceleration due to gravity becomes half.

∴ Weight becomes half, i.e.

W' = W/2 = 200/2 =100 N 

Hence, option 4) is the correct answer.