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 (take g=10ms^-2)

According to question, angle of banking, $\theta ={45}^0$. 

Radius of curved road, r = 90 m and $g=10{\mathrm{ms}}^{-2}.$ 

Let the speed of car on the curved portion of road be $\nu$ . 
For no slip condition

$\mathrm{tan\theta }=\left(\frac{{\mathrm{v}}^2}{\mathrm{rg}}\right)$

$\Rightarrow \mathrm{v}=\sqrt{\mathrm{rg} \mathrm{tan\theta }}$

$\Rightarrow \mathrm{v}=\sqrt{90\times 10\times \tan \left({45}^{\circ }\right)}$

$=\sqrt{900}=30 {\mathrm{ms}}^{-1}$