Question

Optimum speed for turning on a banked road is.

Answer 1

When roads are slanting, they are said to be blanked. While taking a turn, banking of roads is needed to increase safety. At the optimum speed the friction between car tyres and surface of the road is negligible. The optimum speed = $\sqrt {rg\operatorname{Tan} \theta }$ where ‘r’ is the radius of the track and$\theta$ is the angle of banking.

Complete answer:
Optimum speed is the speed with which one can take turns on banked roads without wear and tear.
${v_o} = \sqrt {rg\tan \theta }$, where ${v_o}$ = optimum speed, r= radius, g= gravitational constant. Roads are most often banked for the average speed of vehicles passing over the proper velocity or optimum ‘v’ on a road banked by an angle $\theta$ with the horizontal is given by= $\sqrt {Rg\tan \theta }$ where R is the radius of the curvature of the road, g is the acceleration due to gravity. Hence, the right answer is: $\sqrt {Rg\tan \theta }$.

Note: When a vehicle is moving along a curved path it requires centripetal forces along the curve so that it does not tend to skid over the road. Maximum optimum speed depends on: Radius of the curved path; coefficient of the friction; angle on inclination. We see the angle of banking is independent of the mass of the vehicles.