Two balls of the same material fall in the air. The ratio of the radii of the balls is 4. How many times is the speed

Two balls of the same material fall in the air. The ratio of the radii of the balls is 4. How many times is the speed of the steady-state fall of a large ball? The drag force is proportional to the ball’s cross-sectional area and the square of its velocity.

With a prolonged fall, the movement of the balls will become uniform, since the force of gravity will be balanced by the force of friction

Let’s write down the force expression for the first ball
m1g = k * S1 * V1²;
m1g = k * (n * d1² / 4) * V1²;

for the second
m2g = k * S2 * V2²,
m2g = k * (n * d2² / 4) * V2²;

Find the ratio of the first to the second
m1 / m2 = (d1 * V1) ² / (d2 * V2) ².

The ratio of masses is proportional to the cube of their radii
R1³ / R2³ = (V1 / (4 * V2)) ²;
16/64 = (V1 / V2) ²;
V1 / V2 = √ (1/4) = 1/2.

Answer: 2 times.