AQA AS Level Physics Paper 2, November 2021: Question 22

1 mark · Medium difficulty · Multiple Choice

Identify which diagram correctly shows the position of the centre of mass for two uniform spheres of masses 3 kg and 4 kg joined by a rod of negligible mass.

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Question

Multiple choice question with four diagrams labeled A, B, C, and D showing two spheres P (mass 3 kg) and R (mass 4 kg) separated by distance L. Diagram A shows Q at a distance 3L/7 from P, diagram B shows Q at L/2, diagram C shows Q at 4L/7 from P, and diagram D shows Q at 2L/3 from P.
Question text

22 P and R are uniform spheres of mass 3 kg and 4 kg respectively.

P and R are joined by a rod of negligible mass.

The distance between their centres is L.

The centre of mass of this system is at Q.

Which diagram shows the position of the centre of mass?

[1 mark]

A B

C D

A

B

C

D

Mark scheme

Show the mark scheme Mark scheme indicating the correct answer is C, which shows the centre of mass Q positioned at a distance of 4L/7 from sphere P.

22 C

How to answer it

Centre of Mass Position

What this question tests

This question assesses your understanding of the centre of mass in a system of particles and your ability to apply the principle of moments (or weighted averages) to determine where the centre of mass lies relative to objects of different masses.

Question 22 Analysis

Determining the position of Q for spheres P (3 kg) and R (4 kg) separated by distance L

✅ Correct Answer: C

Diagram C is correct because the centre of mass Q is located at a distance of 4L/7 from sphere P (and 3L/7 from sphere R).

💡 Key Knowledge

  • The centre of mass is always located closer to the heavier mass.
  • Since sphere R (4 kg) is heavier than sphere P (3 kg), Q must be closer to R than to P.
  • Distance from P to Q must be greater than half of L ( L/2 ).

🧠 Exam Technique

  • Elimination: Immediately rule out Diagram B ( L/2 implies equal masses) and Diagram D ( 2L/3 would incorrectly favour P or miscalculate proportions).
  • Check fractions: Total mass = 3 + 4 = 7 kg. The denominators in the correct distances must be 7. This immediately narrows choices down to A and C.

❌ Common Errors

  • Choosing Diagram A ( 3L/7 from P): Students often invert the fractions, mistakenly placing the centre of mass closer to the lighter mass (P).
  • Guessing blindly between A and C without recalling that the centre of mass pulls toward the heavier object.

📐 Step-by-Step Calculation (The Principle of Moments)

To find the exact distance $x$ from the centre of P to the centre of mass Q, take moments about P:

  1. Condition for equilibrium: Sum of clockwise moments = Sum of anticlockwise moments about Q.
  2. Let distance from P to Q be x . Therefore, distance from Q to R is L - x .
  3. Equate moments about Q: 3 × x = 4 × (L - x)
  4. Expand the bracket: 3x = 4L - 4x
  5. Rearrange for x: 7x = 4L → x = 4L/7
🎯 1 Mark awarded for selecting option C.

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, November 2021. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.