Question

1. Find the distance between the two stones each of mass 2 kg so that the gravitational force between them is 1 N.

2. The gravitational force between two objects is 100 N. How should the distance between

these objects change so that the force between them becomes 50 N?​

Answer 1

Solution :

(1)

As per the given data ,

• m 1 = m 2  = 2 kg
• Force = 1 N

The force acting between the two objects placed distance r apart on the surface of the earth is given by ,

$\implies \mathtt{F = G m 1 m 2 / r ^2}$

On rearranging ,

⇒ r ² = G m 1 m 2 / F

⇒ r² = 6.67 x 10- ¹¹ x 2 x 2 / 1

⇒ r ² = 2.668 x 10-¹⁰

⇒ r = 1.633 x 10-⁵ m

_______________

(2)

Given ,

• F 1 = 100 N
• F 2 = 50 N

As per the formula ,

$\implies \mathtt{F = G m 1 m 2 / r ^2}$

From this relation we can conclude that ,

⇒ F ∝ 1 / r ²

Hence ,

⇒ F 1 / F 2 = (r 2 / r 1)²

⇒ r 2 / r 1 =√ F 1 / F2

⇒ r 2 / r 1 = √100 / 50

⇒ r 2 / r 1 = √2

Hence ,

⇒ r 2 = √2 r 1