AS Daily A Level Physics question
In a viscosity experiment, two solid spheres of equal radius are dropped one at a time into a tall cylinder of oil. The steel sphere S has weight 2.0 N in air and the plastic sphere P has weight 1.0 N in air. The upthrust from the oil on either sphere is 0.20 N. For these sizes and speeds in this oil, the resistive force is approximately proportional to speed. After release, each reaches a terminal speed. Compared with P, what is the terminal speed of S?
Answer
The correct answer is D.
Correct: D — Larger by a factor of about 2.25, since at terminal speed the drag equals (weight − upthrust) and here drag is proportional to speed. For S, (2.0 − 0.20) N = 1.80 N; for P, (1.0 − 0.20) N = 0.80 N, so the ratio of terminal speeds is 1.80/0.80 ≈ 2.25. A is wrong because terminal speed depends on the balance of forces; with equal size the upthrust is the same, but different weights give different (weight − upthrust) and thus different terminal speeds. B is wrong because upthrust depends on displaced volume (same radius), not on weight, so it is the same for both spheres. C is wrong because the question states drag is proportional to speed for these conditions; the √2 factor comes from incorrectly assuming drag ∝ v^2 here. D is correct as shown by the (weight − upthrust) ratio and the stated proportionality of drag to speed.