Q 12-01-053JEE MainJEE Main 2024 (6 Apr, Shift 2)Medium
Two identical conducting spheres $P$ and $S$ with charge $Q$ on each repel each other with a force of $16\ \text{N}$. A third identical uncharged conducting sphere $R$ is successively brought in contact with the two spheres. The new force of repulsion between $P$ and $S$ is
Answer: (B) $6\ \text{N}$
$R$ touches $P$: each gets $\dfrac Q2$. $R$ then touches $S$: each gets $\dfrac{Q/2 + Q}{2} = \dfrac{3Q}{4}$.
$$F' = 16\times\frac{(Q/2)(3Q/4)}{Q^2} = 16\times\frac38 = 6\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics