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Class 11  Ā»  Physics  Ā»  Kinematics

Uniform Circular Motion - UNSOLVED PRACTICE SET

Class 11

Chapter: Kinematics | Topic: Uniform Circular Motion

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Study Material.
Class 11

UNIFORM CIRCULAR MOTION - UNSOLVED PRACTICE SET

Topic: Uniform Circular Motion

Time: 40 mins | Marks: 30 | Difficulty: Medium

SECTION NAME

Q1. In uniform circular motion, the velocity vector is:

  1. Constant in magnitude and direction
  2. Constant in magnitude but changes in direction
  3. Changes in magnitude but constant in direction
  4. Changes in both magnitude and direction

Q2. The acceleration in uniform circular motion is directed:

  1. Along the tangent to the circle
  2. Radially outward from the centre
  3. Radially inward towards the centre
  4. Perpendicular to the plane of motion

Q3. The time taken to complete one full revolution in uniform circular motion is called:

  1. Frequency
  2. Time period
  3. Angular velocity
  4. Linear velocity

Q4. The relation between linear velocity v, angular velocity Ļ‰, and radius r is:

  1. v = Ļ‰/r
  2. v = Ļ‰r
  3. v = r/Ļ‰
  4. v = Ļ‰Ā²r

Q5. A particle moves in a circle of radius 2 m with a speed of 4 m/s. Its centripetal acceleration is:

  1. 2 m/sĀ²
  2. 4 m/sĀ²
  3.  8 m/sĀ²
  4. 16 m/sĀ²

Q6. In uniform circular motion, the angle between the velocity vector and the acceleration vector is:

  1. 0Ā°
  2. 45Ā°
  3. 90Ā°
  4. 180Ā°

Short Answer Questions

Q7. Define uniform circular motion. Why is it called "accelerated motion" even though the speed remains constant?

Q8. Derive the expression for centripetal acceleration in uniform circular motion.

Q9. A stone tied to a string is whirled in a horizontal circle of radius 1 m at 2 revolutions per second. Calculate:

(a) The angular velocity

(b) The linear speed of the stone

Q10. In your school merry-go-round, a child sits 2 m from the centre. If the merry-go-round completes one rotation every 4 seconds, calculate the child's centripetal acceleration.

Q11. Distinguish between angular velocity and linear velocity in circular motion. How are they related?

Q12. A satellite orbits the Earth at a height where the orbital period is 24 hours. What is special about this orbit? What is it called?

Long Answer Questions

Q13. Explain uniform circular motion in detail. Derive expressions for:

(i) Angular velocity

(ii) Linear velocity

(iii) Centripetal acceleration

(iv) Time period and frequency

Discuss why uniform circular motion is an example of accelerated motion despite constant speed.

Q14. A particle moves in a circle of radius 5 m with a constant speed of 10 m/s.

(a) Calculate the angular velocity.

(b) Calculate the centripetal acceleration.

(c) Calculate the time period of revolution.

(d) Calculate the frequency.

(e) Draw a diagram showing the velocity and acceleration vectors at two different points on the circle.

Q15. Analyse the following situations involving circular motion:

(i) A car taking a turn on a level road

(ii) A stone tied to a string being whirled vertically

(iii) An electron revolving around the nucleus

For each case, identify the force providing the centripetal acceleration and discuss what would happen if this force were removed.

Application-Based Problems

Q16. The Moon orbits the Earth in a nearly circular orbit of radius 3.84 Ɨ 10āø m with a period of 27.3 days.

(a) Calculate the angular velocity of the Moon in rad/s.

(b) Calculate the linear speed of the Moon.

(c) Calculate the centripetal acceleration of the Moon.

(d) Compare this acceleration with g = 9.8 m/sĀ². What does this tell you about why the Moon doesn't fall to Earth?

Q17. A motorcyclist rides around a circular track of radius 50 m at a constant speed.

(a) If the maximum frictional force that can provide centripetal acceleration is 5000 N and the total mass (rider + motorcycle) is 250 kg, what is the maximum safe speed?

(b) If the motorcyclist doubles the speed, by what factor does the required centripetal force increase?

(c) What happens if the motorcyclist tries to take the turn at a speed greater than the maximum safe speed?

(d) Why are banked tracks used in race circuits?

Q18. A satellite is to be placed in a circular orbit around the Earth at a height of 600 km above the Earth's surface. (Radius of Earth = 6400 km, g at surface = 9.8 m/sĀ²)

(a) Calculate the radius of the orbit.

(b) Using the relation g' = g(R/R+h)Ā², calculate the acceleration due to gravity at the orbital height.

(c) This acceleration provides the centripetal acceleration for the satellite. Calculate the orbital speed.

(d) Calculate the time period of the satellite.

(e) How many times does the satellite orbit the Earth in one day?


Total: 30 Marks | Time: 40 mins

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