Vertical Circular Motion – Rankers Physics

Vertical Circular Motion: Practice Problem & Solution

Assertion (A): A bob of mass \( m \) is freely suspended from a light rod of length \( L \). The minimum speed given to bob at lowest position to complete vertical circle is \( 2\sqrt{gL} \). Reason (R): A bob of mass \( m \) is freely suspended from a light string of length \( L \). If bob is given speed \( \sqrt{6gL} \) at the lower position then bob will be complete vertical circle.
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 Vertical Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:

For a mass attached to a rod, the minimum speed at the lowest point to complete a vertical circle is \( v_{min} = 2\sqrt{gL} \). So (A) is true. For a mass on a string, if \( v_{bottom} = \sqrt{6gL} \), the speed at the top will be \( v_{top} = \sqrt{2gL} \). Since \( v_{top} > \sqrt{gL} \), the circle will be completed. So (R) is true. However, they describe different conditions, so (R) is not a correct explanation of (A).

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