Find the maximum possible speed for the given angle of banking ‘θ’ on a curved road of radius

Question

Find the maximum possible speed for the given angle of banking \('\theta'\) on a curved road of radius r having coefficient of friction \(\mu\).

(1) \(v_{max} = \sqrt{\frac{gr(\mu + \tan\theta)}{(1 - \mu\tan\theta)}}\)

(2) \(v_{max} = \sqrt{\frac{gr(\mu - \tan\theta)}{(1 - \mu\tan\theta)}}\)

(3) \(v_{max} =\sqrt{\frac{gr(1 + \mu\tan\theta)}{(1 - \mu\tan\theta)}}\)

(4) \(v_{max} = \sqrt{\frac{gr(\mu - \tan\theta)}{(1 + \mu \tan\theta)}}\)

Answer 1

Correct option is : (1) \(v_{max} = \sqrt{\frac{gr(\mu + \tan\theta)}{(1 - \mu\tan\theta)}}\) 

\(\Rightarrow N = \frac{mv^2}{r}\sin \theta + mg \cos \theta\) 

Also \(\frac{mv^2}{r}\cos \theta = \mu N+ mg \sin \theta\)