The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which

Question 101 of 108

Q. The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which a car can be driven safely along it is 25 m/sec.

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2024Subjective· 3mImportance★★★★★

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Banking angle needed for a given maximum safe speed (frictionless case).

For a road banked at angle $\theta$ , the maximum speed at which a vehicle can be driven safely (assuming friction is not relied upon) is

$v_{max} = \sqrt{rg\tan\theta} \quad\Rightarrow\quad \tan\theta = \frac{v_{max}^2}{rg}$

With $v_{max}=25$ m/s, $r=200$ m, $g=9.8$ m/s²: …

Q.The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which a car can be driven safely along it is 25 m/sec.