UET Lahore ECAT Physics Circular Motion — Set 3

UET Lahore ECAT Physics Circular Motion — Set 3

1. Question 1

   Q1. A particle is moving in a circular path with a radius of 3 m and a constant speed of 6 m/s. What is its period?

   • A) π s
   • B) 2π s
   • C) 3π s
   • D) 4π s

   Answer: 3π s

   Explanation: Period is given by T = 2πr / v = 2π(3) / 6 = π s, but v = rω = r(2π / T), so T = 2πr / v = 2π(3) / 6 = π s.

2. Question 2

   Q2. A cyclist is moving around a circular track of radius 50 m at a speed of 15 m/s. What is his angular speed?

   • A) 0.1 rad/s
   • B) 0.2 rad/s
   • C) 0.3 rad/s
   • D) 0.4 rad/s

   Answer: 0.3 rad/s

   Explanation: Angular speed is given by ω = v / r = 15 / 50 = 0.3 rad/s.

3. Question 3

   Q3. A body is moving in a circular path with a constant speed. What is the magnitude of its average acceleration over one complete revolution?

   • A) Zero
   • B) v² / r
   • C) 2v² / r
   • D) v² / (2r)

   Answer: Zero

   Explanation: Average acceleration over one complete revolution is zero as the initial and final velocities are the same.

4. Question 4

   Q4. A particle is moving in a circular path with a radius of 4 m and an angular velocity of 2 rad/s. What is its linear speed?

   • A) 4 m/s
   • B) 6 m/s
   • C) 8 m/s
   • D) 10 m/s

   Answer: 8 m/s

   Explanation: Linear speed is given by v = rω = 4 * 2 = 8 m/s.

5. Question 5

   Q5. A cyclist is moving around a circular track of radius 80 m at a speed of 20 m/s. What is his angular speed?

   • A) 0.25 rad/s
   • B) 0.5 rad/s
   • C) 0.75 rad/s
   • D) 1 rad/s

   Answer: 0.25 rad/s

   Explanation: Angular speed is given by ω = v / r = 20 / 80 = 0.25 rad/s.

6. Question 6

   Q6. A body is moving in a circular path with a constant speed. What is the change in its kinetic energy over one complete revolution?

   • A) Zero
   • B) Positive
   • C) Negative
   • D) Maximum

   Answer: Zero

   Explanation: Kinetic energy remains constant as the speed is constant, ΔKE = 0.

7. Question 7

   Q7. A particle is moving in a circular path with constant speed. What is the direction of its acceleration?

   • A) Towards the center
   • B) Away from the center
   • C) Tangential to the circle
   • D) Perpendicular to the plane of the circle

   Answer: Towards the center

   Explanation: The acceleration is directed towards the center due to the change in direction of velocity, given by v² / r.

8. Question 8

   Q8. What is the minimum speed required for a particle to complete a vertical circle of radius r?

   • A) √(gr)
   • B) √(5gr)
   • C) √(3gr)
   • D) √(2gr)

   Answer: √(5gr)

   Explanation: Minimum speed at the bottom is √(5gr) to complete the loop, derived from energy conservation and centripetal force.

9. Question 9

   Q9. What is the work done by the centripetal force on a particle moving in a circular path?

   • A) Positive
   • B) Negative
   • C) Zero
   • D) Depends on the radius

   Answer: Zero

   Explanation: Centripetal force is perpendicular to displacement, so work done is zero, given by W = F * d * cos(90°) = 0.

10. Question 10

    Q10. A cyclist is moving on a circular track with a speed of 10 m/s. If the radius is 20 m, what is the angle of banking?

    • A) tan^-1(0.5)
    • B) tan^-1(1)
    • C) tan^-1(2)
    • D) tan^-1(0.25)

    Answer: tan^-1(0.5)

    Explanation: The angle of banking is given by tan(θ) = v² / rg = 100 / (20 * 10) = 0.5.

11. Question 11

    Q11. What is the ratio of the kinetic energies of two particles moving in circular paths with radii r and 2r, if their time periods are the same?

    • A) 1 : 2
    • B) 1 : 4
    • C) 1 : 1
    • D) 2 : 1

    Answer: 1 : 4

    Explanation: T = 2πr / v, so v ∝ r. KE = 0.5mv² ∝ r². Thus, KE ratio is (r / 2r)² = 1 / 4.

12. Question 12

    Q12. A particle is moving in a circular path with a constant angular acceleration. What is the angular displacement in the first 2 seconds if the initial angular velocity is 0?

    • A) α
    • B) 2α
    • C) 0.5α
    • D) 2α (2)

    Answer: 2α

    Explanation: θ = ω₀t + 0.5αt² = 0 + 0.5α(2)² = 2α.

13. Question 13

    Q13. What is the centripetal acceleration of a particle moving in a circular path of radius 50 cm with a speed of 5 m/s?

    • A) 25 m/s²
    • B) 50 m/s²
    • C) 10 m/s²
    • D) 100 m/s²

    Answer: 50 m/s²

    Explanation: a = v² / r = (5)² / 0.5 = 50 m/s².

14. Question 14

    Q14. A car is moving on a circular track. If its speed is increasing, what is the direction of the net force acting on it?

    • A) Towards the center
    • B) Away from the center
    • C) Tangential to the circle
    • D) At an angle to the radius

    Answer: At an angle to the radius

    Explanation: The net force has a radial component (centripetal force) and a tangential component (due to increasing speed).

15. Question 15

    Q15. What is the maximum velocity for a car to move on a circular banked road without skidding?

    • A) √(rg tan(θ))
    • B) √(rg / tan(θ))
    • C) √(rg sin(θ))
    • D) √(rg cos(θ))

    Answer: √(rg tan(θ))

    Explanation: The maximum velocity is given by √(rg tan(θ)), derived from the components of normal reaction and friction.

16. Question 16

    Q16. A cyclist is moving on a circular track. If the radius of the track is 40 m and the coefficient of friction is 0.2, what is the maximum speed?

    • A) 8 m/s
    • B) 10 m/s
    • C) 12 m/s
    • D) √(80) m/s

    Answer: √(80) m/s

    Explanation: Maximum speed is given by √(μrg) = √(0.2 * 40 * 10) = √80 m/s.

17. Question 17

    Q17. What is the angular velocity of a particle moving in a circular path if its linear speed is 10 m/s and the radius is 2 m?

    • A) 5 rad/s
    • B) 10 rad/s
    • C) 20 rad/s
    • D) 2 rad/s

    Answer: 5 rad/s

    Explanation: ω = v / r = 10 / 2 = 5 rad/s.

18. Question 18

    Q18. What is the time period of a particle moving in a circular path if its angular velocity is 2π rad/s?

    • A) 1 s
    • B) 2 s
    • C) 0.5 s
    • D) 4 s

    Answer: 1 s

    Explanation: T = 2π / ω = 2π / 2π = 1 s.

19. Question 19

    Q19. A car is moving on a circular track. If the radius is 100 m and the coefficient of friction is 0.5, what is the maximum speed?

    • A) √(500) m/s
    • B) 10 m/s
    • C) 20 m/s
    • D) √(1000) m/s

    Answer: √(500) m/s

    Explanation: Maximum speed is given by √(μrg) = √(0.5 * 100 * 10) = √500 m/s.

20. Question 20

    Q20. What is the centripetal force acting on a particle of mass 2 kg moving in a circular path of radius 1 m with a speed of 5 m/s?

    • A) 25 N
    • B) 50 N
    • C) 10 N
    • D) 20 N

    Answer: 50 N

    Explanation: F = mv² / r = 2 * (5)² / 1 = 50 N.