Question

The gravitational force between two objects is F. If masses of both the objects are halved without altering the distance between them, then the gravitational force would become

• A. F/4
• B. F/2
• C. F
• D. 2F

Answer 1

Answer: (A)

F/4

Answer 2

The gravitational force $F$ between two objects with masses $m_1$ and $m_2$ separated by a distance $r$ is given by Newton's Law of Universal Gravitation: $F = \frac{G m_1 m_2}{r^2}$ where $G$ is the gravitational constant.

In the new scenario, the masses of both objects are halved, so the new masses are $m_1' = \frac{m_1}{2}$ and $m_2' = \frac{m_2}{2}$. The distance $r$ remains unchanged.

The new gravitational force $F'$ is: $F' = \frac{G m_1' m_2'}{r^2} = \frac{G \left(\frac{m_1}{2}\right) \left(\frac{m_2}{2}\right)}{r^2}$ $F' = \frac{G \frac{m_1 m_2}{4}}{r^2} = \frac{1}{4} \left(\frac{G m_1 m_2}{r^2}\right)$

Since $F = \frac{G m_1 m_2}{r^2}$, we can substitute $F$ into the equation for $F'$: $F' = \frac{1}{4} F$

Therefore, the gravitational force would become $F/4$.