Question

F is gravitational force between two bodies of equal mass M. Which pair has the same force F acting between them for the new masses at same distance?

• A. $M$ & $2M$
• B. $M$ & $3M$
• C. $M$ & $\frac{M}{2}$
• D. $\frac{M}{2}$ & $2M$

Answer 1

The correct option is D $\frac{M}{2}$ & $2M$

Let $M_1$ and $M_2$ be the masses of two objects and $R$ be the distance between them.
The gravitational force, $F=\frac{G{M}_1{M}_2}{R^2}$, where $G$ is the universal gravitational constant.
Since $G$ and $R$ are constant,
$F\propto M_1{M}_2$

When $M_1=M$ and $M_2=M/2$,
$F^{\prime }=F/2$

When $M_1=M$ and $M_2=3M$,
$F^{\prime }=3F$

When $M_1=M$ and $M_2=2M$,
$F^{\prime }=2F$

When $M_1=M/2$ and $M_2=2M$,
$F^{\prime }=F$