Circular Motion with Tangential Acceleration – Rankers Physics

Non Uniform Circular Motion: Practice Problem & Solution

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 \(= v^2/R\).
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

Short Solution (Best for NEET):

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

With constant tangential acceleration \(a_t\) and increasing speed \(v\), centripetal acceleration \(a_c = v^2/R\) increases. The angle \(phi\) between resultant and tangential acceleration follows \(tan\phi = a_c/a_t\), so \(\phi\) increases. Thus (A) is true. (R) correctly defines these accelerations, providing the basis for (A).

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Your email address will not be published.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 particle moves in a circular path so that its distance travel varies with time \(t\) as \(s = 3t^2 + 6t\). Then its acceleration at \(t = 1\text{ sec.}\) is (radius of path is \(12\text{ m}\)) -
2. A cyclist is moving with speeding up itself in a circular track then work done by net force on cyclist will be :
3. 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.  
4. Assertion (A): A body tied to an end of a string is whirled along a vertical circle with such a velocity at the lowest point that, at some position, tension in the string is zero but the speed at the position is non-zero. The body will leave the circular path at the position of zero tension. Reason (R): In vertical circular motion, so as to cross the highest point along the circle, speed at the highest point, \( v_H geq 0 \).  
5. 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)