A car is negotiating a curved road of radius R. The road is banked at angle $\mathrm{\theta }$. The coefficient of friction between the tyres of the car and the road is ${\mathrm{\mu }}_{\mathrm{s}}$. The maximum safe velocity on this road is

1. $\sqrt{\mathrm{gR}\left(\frac{{\mathrm{\mu }}_{\mathrm{s}}+\mathrm{tan\theta }}{1-{\mathrm{\mu }}_{\mathrm{s}}\mathrm{tan\theta }}\right)}$

2. $\sqrt{\frac{\mathrm{g}}{\mathrm{R}}\left(\frac{{\mathrm{\mu }}_{\mathrm{s}}+\mathrm{tan\theta }}{1-{\mathrm{\mu }}_{\mathrm{s}}\mathrm{tan\theta }}\right)}$

3. $\sqrt{\frac{\mathrm{g}}{{\mathrm{R}}^2}\left(\frac{{\mathrm{\mu }}_{\mathrm{s}}+\mathrm{tan\theta }}{1-{\mathrm{\mu }}_{\mathrm{s}}\mathrm{tan\theta }}\right)}$

4. $\sqrt{{\mathrm{gR}}^2\left(\frac{{\mathrm{\mu }}_{\mathrm{s}}+\mathrm{tan\theta }}{1-{\mathrm{\mu }}_{\mathrm{s}}\mathrm{tan\theta }}\right)}$

A car is negotiating a curved road of radius \(R\). The road is banked at an angle \(\theta\). The coefficient of friction between the tyre of the car and the road is \(\mu_s\). The maximum safe velocity on this road is:
1. \(\sqrt{\operatorname{gR}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)
2. \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)
3. \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}^2}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\operatorname{s}} \tan \theta}\right)}\)
4. \(\sqrt{\mathrm{gR}^2\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)