Coulomb force F versus (1/r^2) graphs for two pairs of point charges (q1 and q2)

Question

Coulomb force F versus \(\left(\frac 1{r^2}\right)\) graphs for two pairs of point charges \(\mathrm{(q_1\ and\ q_2)}\) and \(\mathrm{(q_2\ and\ q_3)}\) are shown in the figure. The ratio of charges \(\left( \frac {q_1}{q_3}\right)\) is:

(A) \(\sqrt 3\)

(B) \(\frac 1{\sqrt 3}\)

(C) \(3\)

(D) \(\frac 13\)

Answer 1

Correct option is (D) \(\frac 13\) 

\(F = \frac {kq_1q_2}{r^2}\)

\(F \ \text{ v/s }\ \frac 1{r^2}\)

\(\frac{kq_1q_2}{kq_2q_3} = \frac{\tan 30^\circ}{\tan 60^\circ}\)

\(\frac{q_1}{q_3} = \frac{\frac 1 {\sqrt 3}}{\sqrt 3}\)

\(\frac{q_1}{q_3} = \frac 1 {\sqrt 3} \times \frac 1{\sqrt 3} \)

\(\frac{q_1}{q_3} = \frac 13\)