Assertion and Reason: Safe Velocity Limit on Roads – Rankers Physics
Topic: Circular Motion
Subtopic: Dynamics of Circular Motion

Assertion and Reason: Safe Velocity Limit on Roads

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

Solution:

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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