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A body is moving in a circle of unit radius. How will the centripetal acceleration 'a' of body change according to its speed?
1. a ∝ v2
2. a ∝ v
3. a ∝ 1/v2
4. a ∝ 1/v

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Correct Answer - Option 1 : a ∝ v2

CONCEPT:

  • Centripetal Force: The force that makes a body to move in a circular motion is known as centripetal force.
    • The direction of this force is always perpendicular to the direction of the velocity.
  • The centripetal force acting on a body of mass 'm' revolving with radius 'r' is:

\(⇒ F = {mv^2\over r}\)

  • Centripetal acceleration: When a body moves in a circular motion, the acceleration that makes the direction of the velocity of the body keep changing is known as centripetal acceleration.
  • Its direction is always towards the center.

\(⇒ F =ma_{cp}= {mv^2\over r}\)

\(⇒ a_{cp}= {v^2\over r}\)

where acp is the centripetal acceleration, v is the speed, and r is the radius of the circle.

EXPLANATION:

Given that body is moving in the unit radius circle, so r = 1

  • The centripetal acceleration is given by

\(⇒ a_{cp}= {v^2\over r}\)

⇒ acp ∝ v2

  • So the correct answer is option 1.

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