Correct Answer - Option 1 : a ∝ v
2
CONCEPT:
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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:
\(⇒ F = {mv^2\over r}\)
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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.