# A car is negotiating a curved road of radius R. The road is banked at an angle . The coefficient of friction between the types of the car and the road is s. The maximum safe velocity on this road is: Option 1) $\sqrt{gR^{2}\frac{\mu_{s}+tan\theta}{1-\mu_{2} tan\theta}}$ Option 2) Option 3) Option 4)

As we learnt in

If friction is also present in banking of road -

$\frac{V^{2}}{rg}=\frac{\mu+tan\theta}{1-\mu tan \theta}$

$\theta=$ angle of banking

$\mu=$ coefficient of friction

V = velocity

- wherein

Maximum speed on a banked frictional road

$V=\sqrt{\frac{rg(\mu+tan\theta)}{1-\mu tan\theta}}$

$V=\sqrt{Rg\frac{\tan \theta +\mu _{s}}{1-\mu _{s}\tan \theta }}$

Option 1)

$\sqrt{gR^{2}\frac{\mu_{s}+tan\theta}{1-\mu_{2} tan\theta}}$

Incorrect

Option 2)

Correct

Option 3)

Incorrect

Option 4)

Incorrect

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