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# Optimum speed for turning on a banked road is. Verified
Hint: 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.
${v_o} = \sqrt {rg\tan \theta }$, 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: $\sqrt {Rg\tan \theta }$.