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A particle moves in a circular path of radius 5 m with a constant speed of 10 m/

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Question: A particle moves in a circular path of radius 5 m with a constant speed of 10 m/s. What is the centripetal acceleration of the particle?

Options:

  1. 2 m/s²
  2. 5 m/s²
  3. 10 m/s²
  4. 20 m/s²

Correct Answer: 10 m/s²

Solution: 

Centripetal acceleration (a_c) = v²/r = (10 m/s)² / (5 m) = 20 m/s².

A particle moves in a circular path of radius 5 m with a constant speed of 10 m/

Practice Questions

Q1
A particle moves in a circular path of radius 5 m with a constant speed of 10 m/s. What is the centripetal acceleration of the particle?
  1. 2 m/s²
  2. 5 m/s²
  3. 10 m/s²
  4. 20 m/s²

Questions & Step-by-Step Solutions

A particle moves in a circular path of radius 5 m with a constant speed of 10 m/s. What is the centripetal acceleration of the particle?
  • Step 1: Identify the formula for centripetal acceleration, which is a_c = v² / r.
  • Step 2: Determine the values needed for the formula. Here, the speed (v) is 10 m/s and the radius (r) is 5 m.
  • Step 3: Substitute the values into the formula: a_c = (10 m/s)² / (5 m).
  • Step 4: Calculate (10 m/s)², which equals 100 m²/s².
  • Step 5: Divide 100 m²/s² by 5 m to find the centripetal acceleration: 100 m²/s² / 5 m = 20 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.
  • Uniform Circular Motion – The motion of an object traveling at a constant speed along a circular path, where the direction of the velocity vector changes continuously.
  • Formula Application – Understanding and applying the formula for centripetal acceleration, a_c = v²/r, where v is the linear speed and r is the radius of the circular path.
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