AQA A-Level Physics Paper 1, June 2023: Question 23

1 mark · Easy difficulty · Multiple Choice

Determine the terminal speed of a falling sphere of mass m given that the resistive force is kv where k is a constant.

Practise this question

Question

Multiple choice question 23 asking for the terminal speed of a sphere of mass m falling with speed v where the resistive force is kv. Four options are provided: A (mg/k), B (km/g), C (kmg), and D (k/mg).
Question text

23 A sphere of mass m falls with speed v.

The resistive force on the sphere is kv, where k is a constant.

What is the terminal speed of the sphere?

[1 mark]

mg

A

k

km

B

g

C kmg

k

D

mg

Mark scheme

Show the mark scheme Mark scheme for question 23 showing the correct answer is A, which corresponds to the expression mg over k.

mg

23 A

k

How to answer it

Terminal Speed of a Falling Sphere

What this question tests

This question assesses your understanding of forces in fluid dynamics, specifically recognising the condition for terminal velocity/speed (balancing forces) and rearranging simple algebraic equations relating weight, resistive forces, and speed.

Question 2.3 • Multiple Choice • 1 Mark

Determining Terminal Speed

✅ Correct Answer: A

The correct option is A ( mg / k ).

💡 Key Knowledge

  • Weight: The downward force acting on the sphere is given by W = mg .
  • Resistive Force: The upward frictional/drag force opposing motion is given as kv .
  • Terminal Condition: At terminal speed, acceleration is zero, meaning the downward driving force equals the upward resistive force ( W = F_drag ).

🧠 Exam Technique

For quick multiple-choice physics questions involving proportionality and definitions:

  1. Write down the physical condition instantly: Accelerating = 0 ⇒ Driving Force = Resistive Force .
  2. Substitute the expressions given in the stem: mg = kv .
  3. Make the target variable ( v ) the subject.

📐 Step-by-Step Derivation

  1. State condition for terminal speed:
    Upward force = Downward force
  2. Substitute known terms:
    kv = mg
  3. Rearrange for terminal speed ( v ):
    v = mg / k

❌ Common Errors & Distractor Analysis

Students under time pressure often guess upside-down ratios or misinterpret algebraic proportionality:

  • Option B ( km / g ) & D ( k / mg ): Inverted relationships resulting from incorrect algebraic transposition. Always check dimensional consistency—speed must increase if mass or gravity increases, and decrease if resistance constant k increases.
  • Option C ( kmg ): Multiplies all terms together instead of equating opposing forces.
Mark Scheme Allocation: 1 mark for selecting option A. No working out required on the paper, but keeping a mental or margin note of mg = kv prevents careless inversion errors.

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.