A car of mass $1000$ kg negotiates a banked curve of radius $90$ m on a frictionless road. If the banking angle is of $45^\circ,$ the speed of the car is:

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. $\sqrt{\mathrm{gR}^2\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}$