JEE Main 2025 — Electrostatics Question with Solution

To find the ratio of the magnitudes of electrostatic force to gravitational force between ions $A$ and $B$, we use the following formulas for electrostatic force ($F_e$) and gravitational force ($F_g$):

$F_e=\frac{k\cdot q_1\cdot q_2}{r^2}$

$F_g=\frac{G\cdot m_1\cdot m_2}{r^2}$

To find the ratio $\frac{F_e}{F_g}$, simplify as follows:

$\frac{F_e}{F_g}=\frac{k\cdot q_1\cdot q_2}{G\cdot m_1\cdot m_2}$

Using the given values:

$k=9\times 10^9{\text{Nm}}^2{\text{C}}^{-1}$

$q_1=6.67\times 10^{-19}\text{C}$

$q_2=9.6\times 10^{-10}\text{C}$

$G=6.67\times 10^{-11}{\text{Nm}}^2{\text{kg}}^{-2}$

$m_1=19.2\times 10^{-27}\text{kg}$

$m_2=9\times 10^{-27}\text{kg}$

The formula becomes:

$\frac{F_e}{F_g}=\frac{9\times 10^9\times 6.67\times 10^{-19}\times 9.6\times 10^{-10}}{6.67\times 10^{-11}\times 19.2\times 10^{-27}\times 9\times 10^{-27}}$

Calculate the result:

$=\frac{10^{-20}}{2\times 10^{-65}}$

This calculation gives the ratio of the electrostatic force to the gravitational force without considering their separation distance $r$, as it cancels out. The value of $P$ mentioned in the prompt can be deduced from the simplified final expression.