Question

Consider a 5kg rock and a 4.5g piece of paper held at the same height above the ground. What is true about the gravitational field at their location and the gravitational force on both objects ?

Answer 1

Answer:

The gravitational field at any point is independent of the objects placed at that point such as a stone or paper.

And, also the gravitational force acting on a body is determined by the intensity of the field at that point.

Explanation:

Given,

The gravitational force between two bodies separated by a distance r is given by the relation,

                              F =  GMm / r²

Where,

                    M - the mass of the Earth

                    m - the mass of the object

                     r - the distance between the center of masses

Let m₁ be the mass of rock. Then force acting on the rock is given by

                                    F = m₁a

The gravitational force between the stone and Earth is given by

                                    F = GMm₁ / r²

Equating these two forces

                                     m₁a = GMm₁ / r²

Canceling out the mass of the stone.

This shows that the force component acceleration is independent of the mass of the stone.

Hence, it implies that the gravitational field at any point is independent of the objects placed at that point such as a stone or paper.

And, also the gravitational force acting on a body is determined by the intensity of the field at that point.