A railway wagon (open at the top) of mass M₁ is moving with speed v₁ along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M₂ and speed becomes v₂. Taking the rain to be falling vertically and water stationary inside the wagon, the relation between the two speeds v₁ and v₂ is:

The correct answer is Option C based on the Law of Conservation of Linear Momentum. In physics, if no external horizontal force acts on a system, its total linear momentum in that direction remains constant.

• Initial State: The wagon has mass M₁ and moves with velocity v₁. The rain falls vertically, meaning its initial horizontal velocity is zero. Thus, the initial horizontal momentum is M₁v₁.
• Final State: As rain accumulates, the total mass of the wagon and water becomes M₂ and it moves with velocity v₂. The final horizontal momentum is M₂v₂.

Since there is no external horizontal force (ignoring friction), the initial momentum must equal the final momentum: M₁v₁ = M₂v₂. As the mass increases (M₂ > M₁), the velocity must decrease (v₂ < v₁) to keep the momentum conserved.