question_answer

If the road is banked and circular, choose the correct option.

A)  There is no need of friction for centripetal force

B)  If \[N\sin \theta <{{F}_{C}},{{({{f}_{s}})}_{\max }}\]must act in the upward direction

C)  If \[N\sin \theta >{{F}_{C}},{{({{f}_{s}})}_{\max }}\]must act in the downward direction

D)  None of the above

Correct Answer: D

Solution :

 Idea For this question student must know about the dynamics for the motion of a car on a circular banked road. If N\[\sin \mathbf{\theta }=\frac{m{{v}^{2}}}{R}\], then there is no need of friction. If N\[\sin \mathbf{\theta }>\frac{m{{v}^{2}}}{R}\], then\[{{f}_{s}}\]will act in upward direction along the inclined surface. \[\Rightarrow \]But\[{{({{f}_{s}})}_{\max }}\]will act for the minimum speed. In the same way if N\[\sin \mathbf{\theta }<\frac{m{{v}^{2}}}{R}\], then\[{{f}_{s}}\]will act in downward direction along the inclined plane. But\[{{({{f}_{s}})}_{\max }}\]ill act for the maximum speed. TEST Edge Different questions could be asked on the same concept. One can replace the banked road from a rotating hemispherical bowl and with the same concept of normal reaction and friction, students can solve this problem.