Question

7 multiple choice 1 point
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 \d/2\, what is the new force between them?
f/4
4f
f
16f
f/16
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Explanation:

Step1: Write 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 \(d/2\)

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

Answer:

B. \(4F\)