Lesson 6.05d-e

6.05d-e Motion in a vertical circle Quiz: OCR Further Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 6.05d-e, Motion in a vertical circle: 20 multiple choice questions for the OCR Further Maths (H245), Unit 3: Mechanics (Y543), written with Revision Ninja.

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The 20 questions

  1. What is the minimum speed at the lowest point for a light string to complete a vertical circle?

    • √(gl)
    • √(3gl)
    • √(5gl)
    • √(4gl)

  2. What is the minimum speed at the highest point for a light string to complete a vertical circle?

    • √(2gl)
    • √(5gl)
    • 0
    • √(gl)

  3. What is the minimum speed at the bottom for a light rigid rod to complete a vertical circle?

    • 3√(gl)
    • √(gl)
    • √(5gl)
    • 2√(gl)

  4. What is the minimum speed at the highest point for a particle on a light rigid rod to complete a circle?

    • √(5gl)
    • √(2gl)
    • 0
    • √(gl)

  5. What condition must be met for a string to become slack during vertical circular motion?

    • Speed becomes zero
    • Tension becomes zero
    • Tension equals weight
    • Reaction becomes zero

  6. What is the difference between bottom tension and top tension for a complete circle with a string?

    • 4mg
    • 5mg
    • 2mg
    • 6mg

  7. A particle slides from rest at the top of a smooth sphere of radius a. At what angle does it leave?

    • arccos(2/3)
    • arccos(1/3)
    • arccos(1/2)
    • arccos(3/4)

  8. A particle slides from rest at the top of a smooth sphere of radius a. What speed does it leave at?

    • √(ga)
    • √(2ga/3)
    • √(2ga)
    • √(ga/3)

  9. What happens to a particle on a string if speed reaches zero before tension reaches zero?

    • Moves in line
    • String slacks immediately
    • Oscillates as pendulum
    • Leaves circular path

  10. What component of weight acts radially outwards when a particle on a string is angle θ to the downward vertical?

    • mg sinθ
    • mg secθ
    • mg tanθ
    • mg cosθ

  11. What is the tangential acceleration of a particle in a vertical circle at angle θ from the downward vertical?

    • -g sinθ
    • -g cosθ
    • g tanθ
    • 0

  12. A particle on a string has speed u at the lowest point. What is its speed v at height h?

    • u - 2gh
    • √(u² - gh)
    • √(u² + 2gh)
    • √(u² - 2gh)

  13. A bead slides on a smooth vertical circular wire. What minimum bottom speed is needed to complete a circle?

    • 3√(gr)
    • √(5gr)
    • √(gr)
    • 2√(gr)

  14. At what point in a vertical circular path is the tension in a light string at its maximum?

    • Horizontal point
    • Midpoint
    • Lowest point
    • Highest point

  15. A particle on a 1m string has speed 6 m s⁻¹ at the bottom. Does it complete a circle?

    • Only at top
    • Only if rigid
    • No
    • Yes

  16. A particle of mass m moves in a vertical circle. What is top string tension T given top speed v?

    • m v² / r - m g
    • m g - m v² / r
    • m v² / r
    • m v² / r + m g

  17. What physical condition determines when a particle inside a smooth circle leaves the surface?

    • Acceleration is constant
    • Velocity is zero
    • Normal reaction is zero
    • Tension is maximum

  18. What is string tension when a particle passing through the horizontal point of its circle has speed v?

    • m v² / r
    • m v² / r + m g
    • m v² / r - m g
    • m g

  19. What happens to a particle on a light string with initial speed u = root(3gl) at the bottom?

    • Stops instantly
    • Stays taut throughout
    • String becomes slack
    • Completes full circles

  20. For a particle moving in a vertical circle of radius r, what expression gives its radial acceleration?

    • d v / d t
    • v² / r
    • v² r
    • v / r

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