Assertion and Reason: Safe Velocity Limit on Roads – Rankers Physics

Dynamics of Circular Motion: Practice Problem & Solution

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.
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 Dynamics of Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true: On an unbanked road, the maximum safe velocity is \( v_{\text{max}} = \sqrt{mu_s gr} \). An increase in friction (\( \mu_s \)) leads to an increased \( v_{\text{max}} \).

Reason (R) is true: Banking of roads provides a component of the normal force for centripetal force, effectively increasing the limiting velocity. (R) is not the correct explanation for (A) as they represent different factors influencing safe velocity.

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