Acceleration in Uniform Circular Motion – Rankers Physics

Uniform Circular Motion: Practice Problem & Solution

Assertion (A): Whenever a particle moves in a circular path with uniform speed, an acceleration exists which is directed towards the centre Reason (R): The net acceleration of a particle in circular motion is always radially inward.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Uniform Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:

In UCM, there is always centripetal acceleration towards the center, even if speed is uniform, due to change in velocity direction. So (A) is true. In UCM, the only acceleration is centripetal, which is radially inward. So (R) is true and explains (A).

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Assertion (A): In uniform circular motion of a body, its linear speed remains constant. Reason (R): In uniform circular motion total acceleration of the body has no radial component.  
2. The kinetic energy \((K)\) of particle moving along a circle of radius \(R\) depends upon the distance covered \(S\) and is given by \(K = aS\) where \(a\) is a constant. Then the centripetal force acting on the particle is:
3. Assertion (A): Infinitesimally small angular displacement is a vector quantity. Reason (R): Angular velocity doesn't depend upon reference frame.  
4. A particle of mass \(m\) is tied to a string of length \(l\) and whirled into a horizontal plane. If tension in the string is \(T\) then the speed of the particle will be: (1999)
5. Two stones of masses m and 2 m are whirled in horizontal circles, the heavier one in a radius r/2 and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is :