Introduction
Assuming the earth to be a sphere of uniform mass density, we can calculate the weight of a body at different depths inside the earth. In this article, we will explore how the weight of a body changes as it moves from the surface to the center of the earth.
Weight at Half the Radius of the Earth
If a body weighs 250 N on the surface of the earth, its weight at a depth equal to half the radius of the earth can be calculated using the formula:
W = (G * M * m) / r^2
Where:
- W is the weight of the body
- G is the gravitational constant
- M is the mass of the earth
- m is the mass of the body
- r is the radius of the earth
Plugging in the values, we get:
W = (6.67 x 10^-11 * 5.97 x 10^24 * m) / (6.38 x 10^6)^2 = 250 N
Solving for m, we find that the mass of the body is approximately 2.17 kg.
Weight at the Center of the Earth
As the body moves towards the center of the earth, its weight decreases. At the center of the earth, the weight of the body can be calculated by the formula:
W = (G * M * m) / (r/2)^2 = 0
Since the distance from the center of the earth is zero, the weight of the body becomes zero at the center.
Conclusion
By assuming the earth to be a sphere of uniform mass density, we have calculated the weight of a body at different depths inside the earth. The weight of the body decreases as it moves towards the center of the earth, eventually becoming zero at the center. This calculation helps us understand the gravitational pull at different depths inside the earth.
