Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $$6:5$$ and their respective masses ratio is $$9:4$$. Then, the ratio of their charges will be

Two charged particles with the same kinetic energy pass through a uniform magnetic field perpendicular to their motion. The ratio of radii is $$6:5$$, and the ratio of masses is $$9:4$$. We need to find the ratio of charges.

The radius of the circular path in a magnetic field is given by $$r = \frac{mv}{qB}$$, and since kinetic energy $$KE = \frac{1}{2}mv^2$$, we have $$v = \sqrt{\frac{2KE}{m}}$$.

Substituting this expression for velocity into the formula for the radius yields $$r = \frac{m}{qB}\sqrt{\frac{2KE}{m}} = \frac{\sqrt{2mKE}}{qB}$$.

Because both particles have the same kinetic energy and experience the same magnetic field, the ratio of their radii simplifies to $$\frac{r_1}{r_2} = \frac{\sqrt{m_1}/q_1}{\sqrt{m_2}/q_2} = \frac{q_2\sqrt{m_1}}{q_1\sqrt{m_2}}$$.

Using the given ratios $$\frac{r_1}{r_2} = \frac{6}{5}$$ and $$\frac{m_1}{m_2} = \frac{9}{4}$$, we substitute to obtain $$\frac{6}{5} = \frac{q_2}{q_1} \times \sqrt{\frac{9}{4}} = \frac{q_2}{q_1} \times \frac{3}{2}$$, which leads to $$\frac{q_2}{q_1} = \frac{6}{5} \times \frac{2}{3} = \frac{4}{5}$$.

It follows that $$\frac{q_1}{q_2} = \frac{5}{4}$$.

Hence, the correct answer is Option B.