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A rabbit runs on a circular path with a constant speed v, and the radius of the circular path is r then the acceleration of rabbit is.

A rabbit runs on a circular path with a constant speed v, and the radius of the circular path is r then the acceleration of rabbit is. Correct Answer v<sup>2</sup>/r

CONCEPT:

  • Uniform circular motion: The movement of a body following a circular path is called a circular motion.
    • The motion of a body moving with constant speed along a circular path is called Uniform Circular Motion.
    • Here, the speed is constant but the velocity changes.
    • For a particle to move along the circular path it should have acceleration acting towards the center, which makes it move in a circular path.
    • As acceleration is perpendicular to the velocity of a particle at every instant, it is only changing the direction of velocity and not magnitude and that’s why the motion is uniform circular motion.
    • This acceleration is centripetal acceleration (or radial acceleration), and the force acting towards the center is called centripetal force.

Formula:

Centripetal acceleration (ac) = ω2r

Angular velocity (ω) = v/r

where, v = velocity, ω = angular velocity, r = radius (m).

EXPLANATION:

  • From the above discussion, it's clear that as speed is constant so motion is uniform circular motion.
  • Force acting towards the center is the centripetal acceleration.

Centripetal acceleration (ac) = ω2r

ac= (v/r)2 × r 

ac = v2/r

The correct option is 4.

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