ECAT (Engineering College Admission) Physics Circular Motion — Set 2

ECAT (Engineering College Admission) Physics Circular Motion — Set 2

1. Question 1

   Q1. A car moves around a circular track of radius 50 m with a speed of 20 m/s. What is its centripetal acceleration?

   • A) 4 m/s²
   • B) 8 m/s²
   • C) 10 m/s²
   • D) 12 m/s²

   Answer: 8 m/s²

   Explanation: Centripetal acceleration is given by a = v² / r = (20)² / 50 = 8 m/s².

2. Question 2

   Q2. The angular velocity of a body is 2 rad/s and its radius is 3 m. What is its linear speed?

   • A) 4 m/s
   • B) 5 m/s
   • C) 6 m/s
   • D) 8 m/s

   Answer: 6 m/s

   Explanation: Linear speed is given by v = rω = 3 * 2 = 6 m/s.

3. Question 3

   Q3. A body is moving in a circular path with a constant speed. What is the work done by the centripetal force?

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

   Answer: Zero

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

4. Question 4

   Q4. A particle is moving in a circular path. If its speed is doubled, what happens to its centripetal acceleration?

   • A) Remains same
   • B) Doubled
   • C) Quadrupled
   • D) Halved

   Answer: Quadrupled

   Explanation: Centripetal acceleration is proportional to v², so doubling the speed quadruples the acceleration, a ∝ v².

5. Question 5

   Q5. The time period of a body moving in a circular path is 2 s. What is its angular velocity?

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

   Answer: π rad/s

   Explanation: Angular velocity is given by ω = 2π / T = 2π / 2 = π rad/s.

6. Question 6

   Q6. A body is moving in a circular path of radius 2 m with an angular velocity of 3 rad/s. What is its linear velocity?

   • A) 5 m/s
   • B) 6 m/s
   • C) 7 m/s
   • D) 8 m/s

   Answer: 6 m/s

   Explanation: Linear velocity is given by v = rω = 2 * 3 = 6 m/s.

7. Question 7

   Q7. The centripetal force on a body is given by F = mv² / r. What is the dimension of this force?

   • A) [MLT⁻²]
   • B) [ML²T⁻²]
   • C) [M²LT⁻²]
   • D) [MLT⁻¹]

   Answer: [MLT⁻²]

   Explanation: The dimension of centripetal force is [MLT⁻²] as it is a force, derived from F = mv² / r.

8. Question 8

   Q8. The radius of a circular path is 4 m and the angular velocity is 2 rad/s. What is the centripetal acceleration?

   • A) 12 m/s²
   • B) 16 m/s²
   • C) 18 m/s²
   • D) 20 m/s²

   Answer: 16 m/s²

   Explanation: Centripetal acceleration is given by a = rω² = 4 * (2)² = 16 m/s².

9. Question 9

   Q9. A body is moving in a circular path. If its angular velocity is doubled, what happens to its linear velocity?

   • A) Remains same
   • B) Doubled
   • C) Quadrupled
   • D) Halved

   Answer: Doubled

   Explanation: Linear velocity is directly proportional to angular velocity, v = rω, so doubling ω doubles v.

10. Question 10

    Q10. The frequency of a body moving in a circular path is 0.5 Hz. What is its time period?

    • A) 1 s
    • B) 2 s
    • C) 3 s
    • D) 4 s

    Answer: 2 s

    Explanation: Time period is given by T = 1 / f = 1 / 0.5 = 2 s.

11. Question 11

    Q11. The angular displacement of a body is π/2 rad in 1 s. What is its angular velocity?

    • A) π/2 rad/s
    • B) π rad/s
    • C) 2π rad/s
    • D) 3π rad/s

    Answer: π/2 rad/s

    Explanation: Angular velocity is given by ω = θ / t = (π/2) / 1 = π/2 rad/s.

12. Question 12

    Q12. A body is moving in a circular path with a constant speed. What is the net force acting on it?

    • A) Zero
    • B) mv² / r
    • C) mrω²
    • D) Both B and C

    Answer: Both B and C

    Explanation: The net force is the centripetal force, given by F = mv² / r = mrω².

13. Question 13

    Q13. The centripetal acceleration of a body is 10 m/s² and its radius is 5 m. What is its speed?

    • A) 5√2 m/s
    • B) 7 m/s
    • C) 10 m/s
    • D) 12 m/s

    Answer: 5√2 m/s

    Explanation: Speed is given by v = √(ar) = √(10 * 5) = √50 = 5√2 m/s.

14. Question 14

    Q14. A body is moving in a circular path. If its radius is halved, what happens to its centripetal acceleration?

    • A) Remains same
    • B) Doubled
    • C) Quadrupled
    • D) Halved

    Answer: Doubled

    Explanation: Centripetal acceleration is inversely proportional to r, a = v² / r, so halving r doubles a if v remains constant, but generally v changes.

15. Question 15

    Q15. The angular velocity of a body is 4 rad/s. What is its frequency?

    • A) 2 / π Hz
    • B) 4 / π Hz
    • C) π / 2 Hz
    • D) 2π Hz

    Answer: 2 / π Hz

    Explanation: Frequency is given by f = ω / (2π) = 4 / (2π) = 2 / π Hz.

16. Question 16

    Q16. A particle moves in a circular path of radius 3 m with a constant speed of 6 m/s. What is its angular velocity?

    • A) 1 rad/s
    • B) 2 rad/s
    • C) 3 rad/s
    • D) 4 rad/s

    Answer: 2 rad/s

    Explanation: Angular velocity is given by ω = v / r = 6 / 3 = 2 rad/s.

17. Question 17

    Q17. A particle moves in a circular path with a 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 centripetal force, given by a = v² / r.

18. Question 18

    Q18. A cyclist is moving around a circular track of radius 100 m at a speed of 10 m/s. What is his centripetal acceleration?

    • A) 0.5 m/s²
    • B) 1 m/s²
    • C) 1.5 m/s²
    • D) 2 m/s²

    Answer: 1 m/s²

    Explanation: Centripetal acceleration is given by a = v² / r = (10)² / 100 = 1 m/s².

19. Question 19

    Q19. A particle is moving in a circular path with a radius of 0.5 m and a constant speed of 2 m/s. What is its angular speed?

    • A) 2 rad/s
    • B) 4 rad/s
    • C) 6 rad/s
    • D) 8 rad/s

    Answer: 4 rad/s

    Explanation: Angular speed is given by ω = v / r = 2 / 0.5 = 4 rad/s.

20. Question 20

    Q20. A car is moving around a circular track of radius 200 m at a speed of 25 m/s. What is its centripetal acceleration?

    • A) 2.5 m/s²
    • B) 3.125 m/s²
    • C) 4 m/s²
    • D) 5 m/s²

    Answer: 3.125 m/s²

    Explanation: Centripetal acceleration is given by a = v² / r = (25)² / 200 = 3.125 m/s².