Question

Gravitational force between two point masses $m$ and $M$ separated by some distance is $F$. Now if a point mass $2m$ is placed next to $m$ in contact with it, the force on $M$ due to $m$ and the total force on $M$ are

• A. $2F,F$
• B. $F,2F$
• C. $F,3F$
• D. $F,F$

Answer 1

The correct option is C $F,3F$

The gravitational force between two particles of masses $m_1$ and $m_2$, separated by a distance $r$ is given by

$F=G\frac{m_1{m}_2}{r^2}$

In the first scenario,

$F=G\frac{Mm}{r^2}$

In the second scenario,

$F^{\prime }=G\frac{M\left(3m\right)}{r^2}=3F$

Hence, the total force on mass $M=3F$

The force between two masses is independent of other masses in the vicinity.

Hence, force on $M$ due to $m$ will still be $F$.

Therefore, option $\left(c\right)$ is correct.

Why this question: To help students understand the Principle of Superposition. Key concept: Principle of Superposition - The gravitational force between two masses is independent of other masses in the vicinity and the net force on a mass is equal to the vector sum of forces by all the masses.