Question

Two particles each of mass $m$ and carrying charge $Q$ are separated by some distance. If they are in equilibrium under mutual gravitational and electrostatic forces, then Q/m (in C/Kg) is of the order of:

• A. ${10}^{-5}$
• B. ${10}^{-10}$
• C. ${10}^{-15}$
• D. ${10}^{-20}$

Answer 1

Answer: (B)

${10}^{-10}$

Given : Gravitational force = Electrostatics force

Let the distance between the rwo charges be $r$.
$\Rightarrow \frac{G\left(m\right)m}{r^2}=\frac{KQ.Q}{r^2}$
$\Rightarrow \frac{G}{K}=\frac{Q^2}{m^2}$
$\Rightarrow \sqrt{\frac{6.67\times {10}^{-11}}{9\times {10}^9}}=\frac{Q}{m}$
$\therefore \frac{Q}{m}$ is the order of ${10}^{-10}$