Two railway trucks of masses m and 3m move towards each other in opposite directions with speeds 2v and v respectively. These trucks collide and stick together. What is the speed of the trucks after the collision?

Explanation

This problem involves an inelastic collision where two railway trucks stick together after colliding. The principle of conservation of momentum is used to solve for the final speed of the combined mass. Initially, the momentum of the system is calculated by considering the direction and magnitude of each truck's momentum:The momentum of the truck with mass 'm' moving at '2v' is 2mv, while the truck with mass '3m' moving at '-v' (opposite direction) has a momentum of -3mv. The total initial momentum therefore is 2mv - 3mv = -mv.After the collision, the trucks stick together, forming a combined mass of 4m. Let the final velocity of this combined mass be 'v_final'. According to conservation of momentum, the total momentum before the collision equals the total momentum after the collision:-mv = 4m × v_finalSolving for v_final gives v_final = -v/4. The negative sign indicates the direction is opposite to the initial direction of the truck with mass 'm', and the magnitude of the speed is v/4.Incorrect options:v/2: This assumes a different distribution of momentum that does not align with the conservation principle.v: This implies no change in velocity, which contradicts the nature of inelastic collisions.5v/4: This results from a miscalculation of momentum distribution, leading to an incorrect final speed.