Question

If the distance between the two bodies is tripled, how will the gravitational force between them change?

Answer 1

Step 1: Applying the inverse square law
- The gravitational force is inversely proportional to the square of the distance: \[ F \propto \frac{1}{d^2} \]
Step 2: Effect of tripling the distance
- If the original distance is \( d \), and it is tripled to \( 3d \), then: \[ F' = G \frac{m_1 m_2}{(3d)^2} \] - This simplifies to: \[ F' = \frac{F}{9} \] Thus, the gravitational force decreases to \(\frac{1}{9}\)th of its original value.