Question

two objects of equal mass \m\ are held a distance \d\ from each other, and the gravitational force between them is \f\. if the distance between the masses becomes \4d\, what is the new force between them? f/16 f/4 4f 16f f

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force is \( F = G\frac{m_1m_2}{d^2} \). Here, \( m_1 = m_2 = m \), so initially \( F = G\frac{m\times m}{d^2}\).

Step2: Calculate the new force when distance is \( 4d \)

When \( d\) becomes \( 4d\), the new force \( F_{new}=G\frac{m\times m}{(4d)^2}\).
Simplify \( F_{new}=G\frac{m^2}{16d^2}\).
Since \( F = G\frac{m^2}{d^2}\), then \( F_{new}=\frac{F}{16}\).

Answer:

A. \( F/16 \)