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

To determine the weight of a body halfway down to the centre of the Earth, we need to understand how gravitational force changes with distance from the Earth's centre. The weight of an object is given by the formula:

W = mg

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

The acceleration due to gravity, g, at a distance r from the centre of the Earth is proportional to the distance from the centre when considering a uniform density Earth model. Mathematically, it is given by:

g' = g \left(\frac{r}{R}\right)

where g' is the gravitational acceleration at distance r, g is the gravitational acceleration at the Earth's surface, and R is the Earth's radius.

If the body is halfway to the Earth's centre, r = \frac{R}{2}. Therefore, the gravitational acceleration at that point would be:

g' = g \left(\frac{\frac{R}{2}}{R}\right) = \frac{g}{2}

Thus, the weight of the body at this point is half of its weight on the surface:

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

Given that the body's weight on the Earth's surface is 200 N:

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

Therefore, the correct answer is 100 N.