Question

① The gravitational force between the two object is 100N. how should the distance between the two be changed so that the force between them becomes 25N ? justify your answer ​

Answer 1

Given :-

▪ The gravitational force between two objects is 100 N.

To Find :-

▪ How should the distance between the two objects be changed so that the force between them becomes 25 N.

Solution :-

Given us the gravitational forces in each cases. It is possible for us to determine the how the distance be changed.

Let the distance between the objects when the force was be d meters. Also, If we observe, the force in the second case becomes one-fourth of the force in first case.

We know,

⇒ F ∝ 1 / d² ...(1)

Where, F is gravitational force, d is the distance between the bodies.

Let the force in first case be F which is equal to 100 N and the distance be d, so In the second case, It is given that the force becomes 100 × 1/4 or F/4

so,

⇒ F / 4 ∝ 1 / (x)²

⇒ F ∝ 4 / x²

⇒ 1 / d² ∝ 4 / x² [ from (1) ]

⇒ x² ∝ 4d²

⇒ x ∝ 2d

Here, The distance between the objects in second case is two times that of in first case.

So, The distance between the objects should be increased twice.