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A particle moves in a circular path with a radius of 2 m and completes one revol

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Question: A particle moves in a circular path with a radius of 2 m and completes one revolution in 4 seconds. What is the linear speed of the particle?

Options:

  1. 1.57 m/s
  2. 3.14 m/s
  3. 6.28 m/s
  4. 12.56 m/s

Correct Answer: 6.28 m/s

Solution: 

Circumference = 2πr = 2π(2) = 4π m. Speed = Distance/Time = 4π/4 = π m/s ≈ 3.14 m/s.

A particle moves in a circular path with a radius of 2 m and completes one revol

Practice Questions

Q1
A particle moves in a circular path with a radius of 2 m and completes one revolution in 4 seconds. What is the linear speed of the particle?
  1. 1.57 m/s
  2. 3.14 m/s
  3. 6.28 m/s
  4. 12.56 m/s

Questions & Step-by-Step Solutions

A particle moves in a circular path with a radius of 2 m and completes one revolution in 4 seconds. What is the linear speed of the particle?
  • Step 1: Identify the radius of the circular path, which is given as 2 meters.
  • Step 2: Use the formula for the circumference of a circle, which is Circumference = 2πr.
  • Step 3: Substitute the radius into the formula: Circumference = 2π(2) = 4π meters.
  • Step 4: Note that the particle completes one full revolution in 4 seconds.
  • Step 5: To find the linear speed, use the formula Speed = Distance / Time.
  • Step 6: Substitute the values into the speed formula: Speed = (4π meters) / (4 seconds).
  • Step 7: Simplify the equation: Speed = π meters/second.
  • Step 8: If needed, approximate π as 3.14 to get the speed in decimal form: Speed ≈ 3.14 m/s.
  • Circular Motion – Understanding the relationship between radius, circumference, and linear speed in circular motion.
  • Speed Calculation – Applying the formula for speed as distance divided by time.
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