Lesson MD4-MD6

MD4-MD6 Conical pendulums and vertical circles Quiz: AQA Further Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson MD4-MD6, Conical pendulums and vertical circles: 20 multiple choice questions for the AQA Further Maths (7367), Unit 3: Optional application 1: mechanics, written with Revision Ninja.

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The 20 questions

  1. For a particle moving in a circle, the acceleration vector always points:

    • Along the tangent to the circle
    • Away from the centre of the circle
    • Perpendicular to the plane of the circle
    • Towards the centre of the circle

  2. The velocity vector of a particle in uniform circular motion is at every instant:

    • Tangent to the circle
    • Zero at the centre of the circle
    • Perpendicular to the tangent
    • Radial, pointing to the centre

  3. For a conical pendulum with one string, the resultant of the tension and weight acts:

    • Vertically upwards
    • Horizontally towards the centre of the circle
    • Vertically downwards
    • Along the string away from the bob

  4. What is the minimum speed at the top of a vertical circle for a particle on a string of length r to just complete the circle?

    • sqrt(2gr)
    • sqrt(g/r)
    • sqrt(gr)
    • Zero

  5. For a particle on a string just completing a vertical circle, what is the tension at the top of the circle?

    • mg divided by r
    • mg
    • Zero
    • 2mg

  6. For a particle on a string moving in a vertical circle, which energy equation links the speed at the bottom (vB) and the top (vT)?

    • vB^2 = vT^2 + gr
    • vB^2 = vT^2 + 4gr
    • vB^2 = vT^2 - 4gr
    • vB = vT + 4gr

  7. In a conical pendulum with a string at angle theta to the vertical, which equation describes the vertical equilibrium?

    • T cos(theta) = mg
    • T = mg sin(theta)
    • T cos(theta) = m r omega^2
    • T sin(theta) = mg

  8. A conical pendulum has a bob of mass m on a string making angle 45 degrees with the vertical. Its speed is v and radius is r. Which expression gives v^2?

    • gr divided by 2
    • g divided by r
    • gr
    • 2gr

  9. A particle moves so that its position vector is r = 2(cos t i + sin t j). What is the magnitude of its acceleration?

    • 2 m/s^2
    • 4 m/s^2
    • cos t m/s^2
    • 1 m/s^2

  10. A conical pendulum has a bob of mass 0.5 kg with the string at 60 degrees to the vertical. Taking g = 10 m/s^2, what is the tension in the string?

    • 5 N
    • 20 N
    • 10 N
    • 2.5 N

  11. A particle has position vector r = 3 cos(2t) i + 3 sin(2t) j metres. What is its velocity at t = 0?

    • (-6, 0) m/s
    • (0, -6) m/s
    • (0, 6) m/s
    • (6, 0) m/s

  12. A particle of mass 0.5 kg on a string of length 0.8 m moves in a vertical circle and has speed 4 m/s at the top. Taking g = 10 m/s^2, what is the tension at the top?

    • 10 N
    • 2.5 N
    • 15 N
    • 5 N

  13. A particle on a string of radius 0.5 m moves in a vertical circle with speed 5 m/s at the bottom. Taking g = 10 m/s^2, does it just complete the circle?

    • Yes, the top speed is 5 m/s
    • Yes, the top speed is sqrt(5) m/s, equal to the minimum
    • No, the top speed is 2.5 m/s
    • No, the top speed is zero

  14. A conical pendulum has string length 1 m and angular speed 4 rad/s. Taking g = 10 m/s^2, what is cos(theta) where theta is the angle with the vertical?

    • 0.16
    • 0.625
    • 1.6
    • 0.4

  15. A particle of mass 0.2 kg hangs from a string and is released from rest with the string horizontal. The string length is 1 m and g = 10 m/s^2. What is its speed at the lowest point?

    • 20 m/s
    • sqrt(10) m/s
    • 10 m/s
    • sqrt(20) m/s

  16. For a particle moving in a vertical circle on a string, what is the difference between the tension at the bottom and the tension at the top?

    • 4mg
    • mg
    • 2mg
    • 6mg

  17. A particle of mass m moves in a horizontal circle of radius r. For the conical pendulum, the horizontal equation of motion is:

    • T cos(theta) = mg
    • T sin(theta) = m v^2 / r
    • T = m g / sin(theta)
    • T sin(theta) = mg

  18. For a conical pendulum with the string at angle theta to the vertical, which expression gives the tension in the string?

    • mg sin(theta)
    • mg cos(theta)
    • mg tan(theta)
    • mg / cos(theta)

  19. A bob on a conical pendulum of mass 2 kg has tension 25 N. What is the vertical component of tension for an angle theta to the vertical?

    • 25 N
    • 20 N
    • 15 N
    • 5 N

  20. In a conical pendulum of string length L at angle theta to the vertical, which expression gives the radius r of the horizontal circle?

    • r = L tan(theta)
    • r = L / sin(theta)
    • r = L sin(theta)
    • r = L cos(theta)

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