Weight at the Surface of the Earth

At the surface of the Earth, the weight of a body is given as 20 N. This weight is the force with which the body is attracted towards the center of the Earth due to gravity. The weight of an object can be calculated using the formula:

Weight = Mass × Acceleration due to gravity

The acceleration due to gravity on the surface of the Earth is approximately 9.8 m/s².

Weight = Mass × 9.8

Unknown weight = Mass × 9.8 ----(1)

Weight at a Height Above the Earth's Surface

When the body is at a height above the Earth's surface, the distance between the center of the Earth and the body increases. This means that the gravitational force acting on the body decreases.

The weight of the body at a height above the Earth's surface can be calculated using the formula:

Weight = Mass × Acceleration due to gravity at that height

The acceleration due to gravity at a height above the Earth's surface can be calculated using the formula:

g' = (g × r²) / (r + h)²

where g is the acceleration due to gravity at the surface of the Earth, r is the radius of the Earth, and h is the height above the Earth's surface.

Weight at a height = Mass × g'

Unknown weight = Mass × g' ----(2)

Solving the Equations

To find the weight of the body at a height of 6400 km above the Earth's surface, we can substitute the given values into equation (2) and solve for the unknown weight.

g = 9.8 m/s²
r = 6400 km = 6400 × 1000 m = 6,400,000 m
h = 6400 km = 6400 × 1000 m = 6,400,000 m

Substituting these values into equation (2):

g' = (9.8 × (6,400,000)²) / ((6,400,000) + (6,400,000))²
= (9.8 × 40,960,000,000) / (12,800,000)²
= (401,408,000,000) / (163,840,000,000)
≈ 2.45 m/s²

Substituting the calculated value of g' into equation (2):

Unknown weight = Mass × 2.45

Since the weight of the body at a height of 6400 km above the Earth's surface is unknown, we cannot determine the exact weight. However, according to the given options, the weight is approximately 5 N, which corresponds to option B.