Question

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?

• A. 150 N
• B. 200 N
• C. 250 N
• D. 100 N

Answer 1

The Correct Option is D

The weight of a body is given by the formula:

W = mg,

where W is the weight, m is the mass of the object, and g is the acceleration due to gravity.

At the surface of the Earth, the acceleration due to gravity is usually denoted as g. However, the acceleration due to gravity changes as we move away from or towards the center of the Earth.

According to the gravitational field variation inside the Earth, the acceleration due to gravity at a distance r from the center of the Earth is given by:

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

where R is the radius of the Earth.

If the body is moved to halfway down to the center, the distance from the center r becomes:

r = \frac{R}{2}

Substituting this into the formula for g_r, we have:

g_{\frac{R}{2}} = g \left(1 - \frac{\frac{R}{2}}{R}\right) = g \left(1 - \frac{1}{2}\right) = \frac{g}{2}

Thus, the acceleration due to gravity halfway to the center is half of that on the surface.

Therefore, the weight of the body at this point becomes:

W' = m \cdot \frac{g}{2} = \frac{W}{2}

Given that the original weight W = 200 N, the new weight is:

W' = \frac{200}{2} = 100 N

Therefore, the correct answer is 100 N.