AQA A-Level Physics Paper 1, June 2024: Question 32

1 mark · Medium difficulty · Multiple Choice

Determine the new periods of a mass-spring system and a simple pendulum when taken to a planet with half the gravitational acceleration of Earth.

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Question

A multiple-choice question numbered 32 asking for the periods of a mass-spring system and a simple pendulum on planet X where gravity is g/2. A table gives four options A, B, C, D with different combinations of T/2, T, 2T, and T multiplied by root 2.
Question text

32 A mass–spring system and a simple pendulum have identical periods of oscillation T when

at the surface of the Earth.

g

Both are taken to planet X where the acceleration due to gravity is .

What are the periods of the mass–spring system and the simple pendulum on X?

[1 mark]

Period of mass–spring system Period of simple pendulum

T

A T 2

B T 2T

C T T 2

D T 2 T

Mark scheme

Show the mark scheme The mark scheme indicating that the correct answer is C, with the period of the mass-spring system being T and the period of the simple pendulum being T multiplied by the square root of 2.

32 C T T 2 AO2

How to answer it

Comparing Periods of Oscillating Systems on Different Planets

What this question tests:

This question assesses your understanding of simple harmonic motion (SHM), specifically how gravitational field strength ( g ) affects the time period of both a mass-spring system and a simple pendulum. It tests your ability to recall respective formula dependencies, apply proportional reasoning, and handle algebraic manipulation under exam conditions (AO2).

Question 3.2 — Multiple Choice (1 Mark)

Exam Breakdown & Solution

✅ Correct Answer: C

Period of mass-spring system: T
Period of simple pendulum: T√(2)

💡 Key Knowledge

  • Mass-Spring System: Time period formula is T = 2π√(m / k) . Note that g is not in this equation!
  • Simple Pendulum: Time period formula is T = 2π√(l / g) . Here, T is inversely proportional to the square root of g ( T ∝ 1 / √(g) ).

📐 Step-by-Step Breakdown

  1. Analyze the Mass-Spring System: Since the period formula T = 2π√(m / k) contains only mass ( m ) and spring constant ( k ), changing the gravitational field strength has zero effect. Therefore, the new period remains T .
  2. Analyze the Simple Pendulum: The pendulum formula is T = 2π√(l / g) . Planet X has a gravitational acceleration of g / 2 .
  3. Substitute g/2 into the equation: T' = 2π√(l / (g / 2)) .
  4. Simplify the fraction: T' = 2π√(2l / g) = √(2) × 2π√(l / g) = T√(2) .

❌ Common Errors & Misconceptions

  • Assuming g affects everything: Many students incorrectly assume that moving to a planet with lower gravity alters the period of a mass-spring system. Always check your formula sheets!
  • Inverting scaling factors: When gravity halves ( g / 2 ), students often mistakenly divide the pendulum period by √(2) instead of multiplying by √(2) . Remember: weaker gravity means slower oscillations (a longer period).

🧠 Exam Technique & Examiner Insights

Top-level candidates quickly eliminate incorrect options by evaluating formula dependencies first. By noting immediately that the mass-spring period is independent of g , options A and D can be discarded straight away, leaving a 50/50 choice between B and C. This strategic elimination saves valuable time in multiple-choice sections.

Mark Scheme Note: Award 1 mark for option C. No working is strictly required for multiple-choice questions, but clear proportional scaling prevents careless algebraic errors.

Topics

Physics · 3.6 Further mechanics and thermal physics (A-level only)

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.