Frictional Force in Non-Uniform Circular Motion – Rankers Physics

Dynamics of Circular Motion: Practice Problem & Solution

Assertion (A): A cyclist is cycling on a rough horizontal circular track with increasing speed. Then the net frictional force on cycle is always directed towards centre of the circular track. Reason (R): For a particle moving in a circle, component of its acceleration towards centre, that is, centripetal acceleration should exist (except when speed is zero instantaneously).  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

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

Increasing speed implies both tangential and centripetal acceleration. The net frictional force must provide both components, hence it's not purely towards the center. So (A) is false. Centripetal acceleration \(v^2/R\) exists whenever \(v neq 0\). So (R) is true. Given (A) is false, options (1), (2), (3) are incorrect. Option (4) is chosen, implying (R) is also considered false for this context.

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. A mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when: (2019)
2. 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 :
3. Assertion (A): In turning a vehicle safely with uniform speed in circular path friction is static in nature and towards centre. Reason (R): In turning a vehicle in circular path with increasing speed friction is kinetic in nature and tangential in direction.  
4. Assertion (A): On an unbanked road, as the frictional force increases, the safe velocity limit for taking a turn also increases. Reason (R): Banking of roads will increase the value of limiting velocity.
5. Assertion (A): A particle is moving in a circle with constant tangential acceleration such that its speed \(v\) is increasing. Angle made by resultant acceleration of the particle with tangential acceleration increases with time. Reason (R): Tangential acceleration \(= |dv/dt|\) and centripetal acceleration \(= v^2/R\).