Two particles, A and B of masses m and 3m, are moving along X and Y axes respectively, with the same speed v. They collide at the origin, and coalesce into one body, after the c ollision. What is the velocity of this coalesced mass ?

Explanation

To solve the problem of two particles A and B colliding and coalescing, we will use the principle of conservation of linear momentum. Let's break down the solution step by step.

### Step 1: Identify the initial momenta of the particles
- Particle A has a mass \( m \) and is moving along the x-axis with speed \( v \).
- Particle B has a mass \( 3m \) and is moving along the y-axis with speed \( v \).

### Step 2: Calculate the momentum of each particle before the collision
- The momentum of particle A along the x-axis is:
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