Eight spherical rain drops of same mass and radius are falling down with a terminal velocity of 6cm/s if they collapse to form 1 big drop what will be its terminal speed? (neglect the buoyant force or buoyancy due to air)

Explanation

When eight smaller spherical drops merge into one larger drop, the volume of the larger drop is the sum of the volumes of the smaller drops. Since volume is proportional to the cube of the radius, the radius of the new drop becomes 2 times the radius of a single smaller drop (since 2^3 = 8). Terminal velocity, v, is proportional to the square of the radius, r, so if the radius doubles, the terminal velocity increases by a factor of 4 (v ∝ r^2). Thus, the new terminal velocity is 4 times the original terminal velocity of 6 cm/s, which is 24 cm/s. Options A, B, and D are incorrect because they do not accurately account for the relationships between volume, radius, and terminal velocity.