# Circular Motion Problems

Here is a set of carefully selected problems on Circular Motion for your practice. All the questions are objective type with single choice correct. The first 10 problems are based on kinematics of circular motion and the remaining are circular dynamics problems. We recommend you to first go through these solved illustrations before proceeding to solve the current set.

1. A particle is moving in a circular path with steady speed. It has
A) a constant velocity
B) a constant acceleration
C) an acceleration of constant magnitude
D) acceleration that varies with time in magnitude

2. A wheel is initially at rest. Its angular velocity increases uniformly and reaches 80 rad/s in 5 seconds. The net angular displacement will be:

3. The second's hand of a watch is 6 cm long. The speed of end point and magnitude of difference of velocities at two perpendicular positions would be:
A) 2π & 0 mm/s
B) 2√2π & 4.44 mm/s
C) 2√2π & 2π mm/s
D) 2π & 2√2π mm/s

4. The magnitude of displacement of a particle moving along the circumference of a circle of radius r with constant angular velocity ω will vary with time t as
A) 2r.sinωt
B) 2r.sin(ωt/2)
C) 2r.cosωt
D) 2r.cos(ωt/2)

5. A particle moves in a circle of radius (20/π)m with a constant tangential acceleration. If the particle is found to move with 80 m/s speed at the end of second revolution after motion has begun, the magnitude of tangential acceleration is:
A) 160π m/s²
B) 40π m/s²
C) 40 m/s²
D) 640π m/s²

6. If angular speed of a disc depends on angle rotated θ as ω = θ² + 2θ, then the angular acceleration α at θ = 1 rad is:
D) None of these

7. A particle moving with a constant speed of 5 m/s in a circle of radius 2m. The acceleration of the particle is:
A) 0
B) 12.5 m/s²
C) 25 m/s²
D) None of these

8. The velocity of a body moving along a circle in the radial direction is
A) 0
B) speed of the body
C) v²/R
D) None of these

9. A particle is moving in a circular track. If the angular velocity, linear velocity, angular acceleration and normal acceleration of the particle at any instant, respectively, are ωvα and aₙ then which of the following relation is NOT correct?
A) ω v
B) ω α
C) ω aₙ
D) v aₙ

10. A particle is moving in a circular path with a speed of 1 m/s. This speed increases at a constant rate of 2 m/s every second. Assuming the radius of the circle described to be 25m, find total acceleration of the particle after 2 seconds.
A) 2 m/s²
B) 25 m/s²
C) √5 m/s²
D) √7 m/s²

11. A body moves along a circular track due to a centripetal force having constant magnitude is an example of motion with
A) constant speed and velocity
B) variable speed and velocity
C) variable speed and constant velocity
D) constant speed and variable velocity

12. If the radii of circular tracks of two bodies of same masses are in the ratio 1:2, then in order to have same radial force (or centripetal force), their speeds should be in the ratio of:
A) 1 : 4
B) 4 : 1
C) 1 : √2
D) √2 : 1

13. A particle is moving along a circular path:
A) Resultant force on the particle must be directed towards the centre.
B) Cross product of the tangential acceleration and angular velocity is zero.
C) Directions of angular acceleration and angular velocity must be the same.
D) The resultant force may be directed towards the centre

14. The ratio of time period of oscillations of a conical pendulum to that of a simple pendulum is (assume the threads are of the same length in the two cases and θ is the angle made by the thread with vertical in case of conical pendulum)
A) cosθ
B) √(cosθ)
C) 1
D) None of these

15. A uniform circular ring of linear mass density λ and radius R is rotating with constant angular velocity ω about its own axis in a gravity free space. Tension in the rotating ring is:
A) zero
B) (1/2)λR²ω²
C) λR²ω²
D) λRω²

16. A road is banked at an angle of 30º (from horizontal) for negotiating a curve of radius 10√3 m. At what velocity will a vehicle experience no friction while negotiating the curve.
A) 54 km/h
B) 72 km/h
C) 36 km/h
D) 18 km/h

17. A man stands on a rough (μ = 0.5) horizontal disc rotating with angular velocity of 5 rad/s. At what distance from centre should he stand so that he does not slip?
A) R ≤ 0.2 m
B) R > 0.2 m
C) R > 0.5 m
D) R > 0.3 m

18. Water in a bucket is whirled in a vertical circle with a thread attached to it. The water doesn't fall down even at the instant the bucket is inverted at the top of its trajectory. We conclude that:
A) mg = mv²/R
B) mg > mv²/R
C) mg < mv²/R
D) None of these