AS Daily A Level Physics question
Two small spheres of the same size and shape are dropped in still air. In this speed range, the drag force on a sphere is approximately proportional to the square of its speed. Sphere B has twice the mass of Sphere A, but identical size and shape. After they each reach terminal velocity, how does B’s terminal speed compare with A’s?
Answer
The correct answer is C.
Correct: C — About 1.4 times larger (sqrt2). At terminal speed, drag balances weight; doubling the weight requires double the drag, so with drag proportional to speed squared the terminal speed increases by sqrt(2) ≈ 1.4. A Twice as large — this would be true only if drag were proportional to speed, not speed squared. B The same — terminal speed depends on weight as well as size/shape; a heavier object needs a larger drag and thus a higher terminal speed. C This follows because doubling weight requires drag to double, and with drag ∝ v^2 the speed must scale by sqrt(2). D Smaller — increasing mass increases the required balancing drag, which is achieved by a higher, not lower, terminal speed.