Question

Two masses $M_1$ and $M_2$, which have a charge $Q_1$ and $Q_2$, respectively are placed at a distance $r$ initially.
If there is no other force acting on the charged particles and they remain at a distance $r$ apart indefinitely, identify which of the following must be true?

• A. Both charges are positive
• B. $Q_1$ is positive and $Q_2$ is negative
• C. $Q_1$ is negative and $Q_2$ is positive
• D. $Q_1=Q_2$
• E. $M_1=M_2$

Answer 1

Answer: (A)

The gravitational force between the two masses is given as $-\frac{G{M}_1{M}_2}{r^2}$

and the electric force between them is given as $\frac{1}{4\pi {ϵ}_0}\frac{Q_1{Q}_2}{r^2}$.

For the masses to remain stationary under these two forces, the net force on each must be zero.

Thus $-\frac{G{M}_1{M}_2}{r^2}+\frac{1}{4\pi {ϵ}_0}\frac{Q_1{Q}_2}{r^2}=0$

$⟹Q_1{Q}_2>0$
Thus they must have same sign.

Hence correct answer is option A.