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A particle moves in a circular path with a radius of 4 m and completes one revol

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Question: A particle moves in a circular path with a radius of 4 m and completes one revolution in 8 seconds. What is the centripetal acceleration?

Options:

  1. 0.5 m/s²
  2. 1 m/s²
  3. 2 m/s²
  4. 4 m/s²

Correct Answer: 1 m/s²

Solution: 

Centripetal acceleration (a_c) = v²/r. First find v = 2πr/T = 2π(4)/8 = π m/s. Then a_c = (π)²/4 = 2.5 m/s².

A particle moves in a circular path with a radius of 4 m and completes one revol

Practice Questions

Q1
A particle moves in a circular path with a radius of 4 m and completes one revolution in 8 seconds. What is the centripetal acceleration?
  1. 0.5 m/s²
  2. 1 m/s²
  3. 2 m/s²
  4. 4 m/s²

Questions & Step-by-Step Solutions

A particle moves in a circular path with a radius of 4 m and completes one revolution in 8 seconds. What is the centripetal acceleration?
  • Step 1: Identify the radius of the circular path, which is given as 4 meters.
  • Step 2: Identify the time taken to complete one revolution, which is given as 8 seconds.
  • Step 3: Use the formula for linear velocity (v) in circular motion: v = (2πr) / T.
  • Step 4: Substitute the values into the formula: v = (2π * 4) / 8.
  • Step 5: Simplify the equation: v = (8π) / 8 = π m/s.
  • Step 6: Now, use the formula for centripetal acceleration (a_c): a_c = v² / r.
  • Step 7: Substitute the value of v and r into the formula: a_c = (π)² / 4.
  • Step 8: Calculate (π)², which is approximately 9.87, and then divide by 4: a_c ≈ 2.5 m/s².
  • Centripetal Acceleration – Centripetal acceleration is the acceleration directed towards the center of a circular path, necessary for an object to maintain circular motion.
  • Velocity in Circular Motion – The linear velocity of an object in circular motion can be calculated using the formula v = 2πr/T, where r is the radius and T is the period of revolution.
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