A particle of mass m₁ and electric charge q starts from rest under the influence of a uniform external electric field E to travel a distance d in time t₁ . If the particle had mass m₂ , it would take time t₂ to travel the same distance. What is the ratio t₁ t₂ ?

Step-by-step solution

Force on the particle is F = qE Acceleration of the particle is a = F m = qE m Using the equation of motion s = ut + 1 2 at^2 with u = 0 and s = d : d = 1 2 ( qE m ) t^2 t = 2dm qE Since d , q , and E are constant, t m t₁ t₂ = m₁ m₂ Answer : m₁ m₂