derive an expression for banking of road with the help of diagram?
For the vehicle to go round the curved track at a reasonable speed without skidding, the greater centripetal force is managed for it by raising the outer edge of the track a little above the inner edge. It is called banking of circular tracks.
Consider a vehicle of weight Mg, moving round a curved path of radius r, with a speed v, on a road banked through angleθ.
The vehicle is under the action of the following forces:

The weight Mg acting vertically downwards

The reaction R of the ground to the vehicle, acting along the normal to the banked road OA in the upward direction
The vertical component R cos θ of the normal reaction R will balance the weight of the vehicle and the horizontal component R sin θ will provide the necessary centripetal force to the vehicle. Thus,
R cosθ = Mg …(i)
$R\mathrm{sin}\theta =\frac{M{v}^{2}}{r}$ ..........(ii)
On dividing equation (ii) by equation (i), we get
$\frac{R\mathrm{sin}\theta}{R\mathrm{cos}\theta}=\frac{M{v}^{2}/r}{Mg}\phantom{\rule{0ex}{0ex}}\mathrm{tan}\theta =\frac{{v}^{2}}{rg}$
As the vehicle moves along the circular banked road OA, the force of friction between the road and the tyres of the vehicle, F = μR, acts in the direction AO.