Two charged particles describe circular paths of the same radius in a uniform magnetic field, which is perpendicular to their plane of motion. If the ratio of their charges is 2:3 and the ratio of their kinetic energies is 4:5 , the ratio of their respective masses will be

Step-by-step solution

The radius of a charged particle moving in a circular path in a uniform magnetic field is given by R = 2mK qB , where m is the mass, K is the kinetic energy, q is the charge, and B is the magnetic field. Squaring both sides, we get R^2 = 2mK q^2 B^2 . Since the radius R and the magnetic field B are the same for both particles, we can write: m₁ K₁ q₁^2 = m₂ K₂ q₂^2 Rearranging to find the ratio of their masses: m₁ m₂ = ( q₁ q₂ )^2 ( K₂ K₁ ) Given that q₁ q₂ = 2 3 and K₁ K₂ = 4 5 , we substitute these values: m₁ m₂ =