A constant force acts on two different masses independently and produces accelerations A₁ and A₂ . When the same force acts on their combined mass, the acceleration produced is

Step-by-step solution

A constant force F produces accelerations A₁ and A₂ on masses m₁ and m₂ , respectively. From Newton's second law: F = m₁ A₁ m₁ = F A₁ F = m₂ A₂ m₂ = F A₂ When the force acts on the combined mass m₁ + m₂ , the acceleration A satisfies: F = (m₁ + m₂)A Substituting both mass expressions yields: F = ( F A₁ + F A₂ )A = F ( 1 A₁ + 1 A₂ )A Dividing both sides by F (nonzero): 1 = ( A₁ + A₂ A₁ A₂ )A Solving for A gives the final result: A = A₁ A₂ A₁ + A₂ The correct choice is C.