Two equal drops of water are falling through air with a steady velocity v. If the drops coalesce, the new velocity will be

To find the new velocity of the coalesced drops, we can use the principle of conservation of momentum.

Step 1: Let's assume the mass of each water drop is m and the initial velocity of each drop is v. Since the drops are equal in size, their masses are the same.

Step 2: The momentum of each drop can be calculated using the formula p = mv, where p is the momentum.

Step 3: The total momentum before the coalescence is the sum of the individual momenta of the drops. So, the total initial momentum is 2mv.

Step 4: When the drops coalesce, they combine to form a single drop with a new mass of 2m.

Step 5: According to the principle of conservation of momentum, the total momentum before and after the coalescence should be the same.

Step 6: Therefore, the total momentum after the coalescence is also 2mv.

Step 7: The new velocity of the coalesced drop can be calculated by dividing the total momentum after the coalescence by the new mass. So, the new velocity (v') is given by v' = (2mv) / (2m).

Step 8: Simplifying the equation, we find that the new velocity (v') is equal to v.

Therefore, the new velocity of the coalesced drops will be the same as the initial velocity, v.