4C.1.2 Motion of a particle in a vertical circle Quiz: Pearson Edexcel Further Maths, Unit 30

The 20 questions

1. A particle on a light inextensible string of length a moves in a complete vertical circle. What is the least speed at the highest point for the string to stay taut?

   • sqrt(5ag)
   • zero
   • sqrt(ag)
   • sqrt(2ag)

2. A particle of mass m on a light string of length a completes a vertical circle. What is the least speed at the lowest point?

   • sqrt(7ag)
   • sqrt(2ag)
   • sqrt(3ag)
   • sqrt(5ag)

3. A particle of mass m on a light string of length a passes the lowest point with speed u. What is the tension there?

   • mu^2/a - mg
   • mg + mu^2/a
   • mu^2/a
   • mg - mu^2/a

4. A particle on a string of length a in a vertical circle has speed u at the lowest point. What is its speed v when the string makes angle theta with the downward vertical?

   • v^2 = u^2 - 2ga(1 - cos theta)
   • v^2 = u^2 + 2ga(1 - cos theta)
   • v^2 = u^2 - ga(1 - cos theta)
   • v^2 = u^2 - 2ga cos theta

5. A particle on a string in a vertical circle has tension T and speed v at angle theta measured from the highest point. Which equation holds along the radius?

   • T + mg sin theta = mv^2/a
   • T = mv^2/a + mg sin theta
   • T + mg cos theta = mv^2/a
   • T - mg cos theta = mv^2/a

6. Which quantity is conserved for a particle moving in a vertical circle on a light string, when only gravity and tension act?

   • Angular velocity at the top
   • Total mechanical energy
   • Linear momentum
   • Radial acceleration

7. For a particle moving in a complete vertical circle on a string, which relation links the speed u at the lowest point and v at the highest point?

   • u^2 = v^2 + 4ga
   • u^2 = v^2 + 2ga
   • u^2 = v^2 - 4ga
   • u = v + 4ga

8. A particle of mass 0.5 kg is on a light string of length 0.8 m and has speed 4 m/s at the highest point of a complete vertical circle (g = 10 m/s^2). What is the tension at that point?

   • 0 N
   • 5 N
   • 10 N
   • 15 N

9. A particle of mass 2 kg is on a light string of length 0.5 m and passes the lowest point of a complete vertical circle with speed sqrt(30) m/s (g = 10 m/s^2). What is the tension at the lowest point?

   • 20 N
   • 60 N
   • 120 N
   • 140 N

10. A particle of mass 2 kg is on a light string of length 0.5 m and moves in a complete vertical circle with speed sqrt(30) m/s at the lowest point (g = 10 m/s^2). What is the tension at the highest point?

    • 40 N
    • 0 N
    • 20 N
    • 60 N

11. A particle of mass 1 kg on a light string of length 1 m is projected from the lowest point with speed 6 m/s and moves in a vertical circle (g = 10 m/s^2). What is its speed when the string makes 60 degrees with the downward vertical?

    • sqrt(46) m/s
    • sqrt(31) m/s
    • sqrt(16) m/s
    • sqrt(26) m/s

12. A particle of mass 1 kg on a light string of length 1 m is projected from the lowest point with speed 6 m/s and moves in a vertical circle (g = 10 m/s^2). What is the tension when the string makes 60 degrees with the downward vertical?

    • 36 N
    • 31 N
    • 25 N
    • 41 N

13. A particle on a light string of length 2 m moves in a vertical circle with speed sqrt(60) m/s at the lowest point (g = 10 m/s^2). What is its speed when level with the centre?

    • sqrt(60) m/s
    • 2 sqrt(5) m/s
    • sqrt(10) m/s
    • sqrt(40) m/s

14. A particle on a light string of length a completes a vertical circle with speed sqrt(3ag) at the highest point. What is its speed at the lowest point?

    • sqrt(11ag)
    • sqrt(3ag)
    • sqrt(5ag)
    • sqrt(7ag)

15. A particle moves in a complete vertical circle on a light string of length 1.2 m (g = 10 m/s^2). Its speed at the lowest point is 8 m/s. What is its speed at the highest point?

    • sqrt(20) m/s
    • sqrt(48) m/s
    • 4 m/s
    • 8 m/s

16. A particle of mass m on a light string of length 1 m moves in a complete vertical circle with tension 7mg at the lowest point (g = 10 m/s^2). What is its speed at the lowest point?

    • sqrt(60) m/s
    • sqrt(50) m/s
    • sqrt(40) m/s
    • sqrt(70) m/s

17. A particle is projected from the lowest point of a light string of length a in a vertical circle. What is the least speed for it to reach the level of the centre with the string still taut?

    • sqrt(3ga)
    • sqrt(2ga)
    • sqrt(ga)
    • sqrt(5ga)

18. A particle of mass 2 kg on a light string of length 1.5 m is at the point level with the centre of the circle, where the tension is 30 N. What is its speed there?

    • sqrt(22.5) m/s
    • sqrt(15) m/s
    • sqrt(45) m/s
    • sqrt(30) m/s

19. A particle of mass m on a light string completes a vertical circle. Its tension at the lowest point is T_b and at the highest point is T_t. What is T_b - T_t?

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

20. A particle on a light string of length 0.4 m is projected from the lowest point with speed sqrt(14) m/s (g = 10 m/s^2). At what angle from the highest point does the tension first become zero?

    • 30 degrees
    • 75 degrees
    • 60 degrees
    • 45 degrees

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