Three identical conducting balls A, B and C, each of mass m, are thrown upward at an angle to the horizontal with an initial speed v in a region of space that has a uniform electric field E downward along with the gravitational field g . A is positively charged, B is uncharged and C is negatively charged. Rank the ranges R of these three balls in increasing order.

Step-by-step solution

The range R of a projectile launched with initial speed v at an angle is given by R = v^2 (2 ) g_ eff , where g_ eff is the effective acceleration acting on the particle in the downward direction. For ball B (uncharged), the only force acting is gravity, so g_ eff, B = g . For ball A (positively charged), the electric force qE acts in the same direction as gravity (downward), so the effective acceleration is g_ eff, A = g + qE m . Since g_ eff, A > g , the range R_A is smaller than R_B . For ball C (negatively char