Two particles of equal mass ' $m$ ' and equal charge ' $q$ ' are separated by a distance of 16 cm . They do not experience any force. The value of $\frac{q}{m}$ is _____ (if ' $G$ ' is the universal gravitational constant and ' $g$ ' is the acceleration due to gravity).

• Correct answer
  A

  $\sqrt{4 \pi \epsilon_0 \mathrm{G}}$
• B

  $\sqrt{\frac{G}{4 \pi \epsilon_0}}$
• C

  $\sqrt{\frac{\pi \epsilon_0}{\mathrm{G}}}$
• D

  $\sqrt{4 \pi \epsilon_0 g}$

Solution

$\begin{aligned} & \text {At equilibrium, } \mathrm{F}_{\mathrm{g}}=\mathrm{F}_{\mathrm{e}} \\ & \Rightarrow \frac{\mathrm{Gm}^2}{(16)^2}=\frac{\mathrm{kq}^2}{(16)^2} \\ & \Rightarrow\left(\frac{\mathrm{q}}{\mathrm{m}}\right)^2=\frac{\mathrm{G}}{\mathrm{k}}=\frac{\mathrm{G}}{\frac{1}{4\pi \varepsilon_0}}=4 \pi \varepsilon_0 \mathrm{G} \\ & \therefore \frac{\mathrm{q}}{\mathrm{m}}=\sqrt{4 \pi \varepsilon_0 \mathrm{G}}\end{aligned}$

Hence, the correct answer is option: 'A'.