Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4 R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch each other is: (Take $k=\frac{1}{4 \pi \epsilon_0}$ and assume $k Q^2 > G m^2$ where $G$ is the Gravitational constant)

• A
  $\sqrt{\frac{k Q^2}{4 m R}\left(1-\frac{G m^2}{k Q^2}\right)}$
• B
  $\sqrt{\frac{k Q^2}{4 m R}\left(1+\frac{G m^2}{k Q^2}\right)}$
• C
  $\sqrt{\frac{k Q^2}{2 m R}\left(1-\frac{G m^2}{k Q^2}\right)}$
• D
  $\sqrt{\frac{k Q^2}{2 m R}\left(1-\frac{G m^2}{2 k Q^2}\right)}$