A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyre 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 of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45^o, the speed of the car is:

1. 20 ms^-1

2. 30 ms^-1

3. 5 ms^-1

4. 10 ms^-1