AS Daily A Level Physics question
In a drop test, a small steel sphere is released from rest directly above a light gate. The gate is first placed a vertical distance d below the release point, then moved to 4d below. Air resistance is negligible and take g = 9.81 m s^-2. Compared to the first reading, what happens to the speed recorded by the gate in the second setup?
Answer
The correct answer is B.
Correct: B — It becomes twice as large. From rest under constant acceleration, the increase in speed depends on how long it has been falling, and the distance fallen grows with the square of time; moving the gate from d to 4d doubles the fall time, so the speed (proportional to time under constant g) doubles. A is wrong because it assumes speed is proportional to distance, but with constant acceleration speed scales with the square root of distance fallen, not directly with distance. B is correct as shown. C is wrong because a factor of about 1.4 would correspond to doubling the distance (√2), not quadrupling it. D is wrong because 9.81 m s^-2 is an acceleration; the speed increase depends on the time to reach the gate, which changes when the distance changes.