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

The correct option is B. $30m/s$

Given,

$r=90m$

$m=1000kg$

$\theta ={45}^0$

$g=10m/s^2$

The speed of car,

The relation between permissible speed and banking angle is,

$tan\theta =\frac{v^2}{rg}$

$\Rightarrow v=\sqrt{rgtan\theta }$

$v=\sqrt{90\times 10\times 1}=30m/s$

Thus the correct option is B.