Lesson 4C.2.2

4C.2.2 Centre of mass of a system of particles Quiz: Pearson Edexcel Further Maths, Unit 31

20 questions

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Lesson 4C.2.2, Centre of mass of a system of particles: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 31: Moments and centres of mass, written with Revision Ninja.

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The 20 questions

  1. For particles of masses m_i at positions x_i, what is the x-coordinate of their centre of mass?

    • sum(m_i) / sum(m_i x_i)
    • sum(m_i x_i) / n
    • sum(x_i) / sum(m_i)
    • sum(m_i x_i) / sum(m_i)

  2. What does the total of m_i x_i over all particles equal?

    • total mass plus the x-coordinate of the centre of mass
    • total mass times the x-coordinate of the centre of mass
    • the sum of the x-coordinates of the particles
    • the x-coordinate of the centre of mass alone

  3. Two particles of equal mass are placed on a straight line. Where is their centre of mass?

    • one third of the way from the first particle
    • at the particle nearer the origin
    • at the origin
    • at the midpoint of the line joining them

  4. How is the centre of mass of a set of particles in a plane found?

    • one formula using the distance of each particle from the origin
    • separate formulas for the x- and y-coordinates, each a weighted average
    • the average of the masses
    • the product of the coordinates divided by the total mass

  5. A particle is added to a system whose centre of mass is G. Where does the new centre of mass lie?

    • on the line joining G and the new particle, between them
    • on the line joining G and the new particle, beyond G
    • at the origin
    • exactly at G

  6. If masses are in kilograms and positions in metres, what are the units of the centre of mass coordinate?

    • kilograms per metre
    • metres
    • kilograms
    • metres per kilogram

  7. Which of these describes a discrete mass distribution?

    • a lamina bounded by a curve
    • a solid sphere of constant density
    • a finite set of particles at given points
    • a uniform rod of constant density

  8. Particles of masses 2 kg and 3 kg are at x = 1 m and x = 4 m. What is the x-coordinate of their centre of mass?

    • 2.8 m
    • 2.2 m
    • 2.5 m
    • 3.4 m

  9. Particles of masses 1 kg at (0,0), 2 kg at (3,0) and 3 kg at (0,6) are placed. What is the centre of mass of the system?

    • (1, 3)
    • (3, 1)
    • (1.5, 2)
    • (2, 2.5)

  10. A system has total mass 12 kg and its centre of mass is at x = 2.5 m. What is the sum of m_i x_i for the system?

    • 14.5
    • 30
    • 9.5
    • 4.8

  11. A 4 kg particle is at x = 0 and a 1 kg particle is at x = 5. What is the x-coordinate of their centre of mass?

    • 1
    • 4
    • 2.5
    • 5

  12. A particle of mass m at x = 1 m and a particle of mass 3 kg at x = 5 m have a combined centre of mass at x = 3.5 m. What is m?

    • 1.5 kg
    • 2.5 kg
    • 1.8 kg
    • 2 kg

  13. Three equal particles sit at the vertices (0,0), (4,0) and (2,6). What is the centre of mass of the system?

    • (4, 2)
    • (2, 3)
    • (2, 2)
    • (3, 2)

  14. Particles of masses 2 kg at x = 0, 3 kg at x = 10 and 5 kg at x = 4 lie on the x-axis. What is the x-coordinate of their centre of mass?

    • 4
    • 6
    • 5
    • 5.5

  15. Masses of 1 kg and 3 kg are at x = 0 and x = 12 respectively. Where is their centre of mass?

    • x = 8
    • x = 3
    • x = 9
    • x = 6

  16. Particles of masses 1, 2, 3 and 4 kg sit at (0,0), (4,0), (4,4) and (0,4). What is their centre of mass?

    • (2.8, 2)
    • (2, 2)
    • (2.5, 2.8)
    • (2, 2.8)

  17. A system of total mass 10 kg has centre of mass at (2, 2). A 2 kg particle at the origin is removed. What is the centre of mass of the remaining 8 kg?

    • (2.5, 2)
    • (2.5, 2.5)
    • (3, 3)
    • (2, 2)

  18. A 2 kg particle is at x = 0 and a 3 kg particle is at x = 5. A 5 kg particle is added on the x-axis so that the new centre of mass is at x = 4. Where is the 5 kg particle?

    • x = 4
    • x = 3
    • x = 6
    • x = 5

  19. Can the centre of mass of a set of particles lie outside the convex hull of the particles?

    • Yes, if one mass is much larger than the rest
    • Yes, whenever the masses are unequal
    • No, it is a weighted average of the positions so it always lies within the hull
    • Yes, if the particles are collinear

  20. A system of total mass 6 kg has centre of mass at (3, 4). A 2 kg particle sits at the origin. Where must the other particle, of mass 4 kg, be for the centre of mass to stay at (3, 4)?

    • (4, 6)
    • (4.5, 5)
    • (4.5, 6)
    • (3, 6)

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