The phenomena in which the edges of the curved roads are raised above the inner edge to provide the necessary centripetal force to the vehicles so that they take a safe turn. The various terminologies used in the case of banking of roads are:

• Banked Turn – It is defined as the turn or change of direction in which the vehicle inclines towards inside.
• Bank Angle – The angle at which the vehicle is inclined is defined as the bank angle.

In the next section, let us look at the formula for the angle of banking.

## Angle of Banking Formula

 The velocity of a vehicle on a curved banked road $v=\sqrt{\frac{(rg(tan\Theta+\mu_s))}{1-\mu_S\,tan\theta}}$ For a given pair of roads, and tyre $\mu_s=tan\lambda$, where $\lambda$ is the angle of friction, the velocity of a vehicle on a curved banked road is $v=\sqrt{rg\,tan(\Theta+\lambda)}$ The safe velocity on an unbanked road is given by the expression $v_{max}=\sqrt{\mu\times r\times g}$ The expression for the angle of banking of road is given by $\Theta=\tan^{-1}\frac{v^2}{rg}$ The expression for the safe velocity on the banked road is given by $v_{max}=\sqrt{rg\,\tan\Theta}$ The expression for the angle of banking $\Theta=\tan^{-1}\frac{v^2}{rg}$

Roads are most often banked for the average speed of vehicles passing over them. Nevertheless, if the speed of a vehicle is lesser or more than this, the self-adjusting state friction will operate between tyre and road and vehicle will not skid.

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#### Practise This Question

A wire of length L is bent in the form of a circular coil and current i is passed through it. If this coil is placed in a magnetic field then the torque acting on the coil will be maximum when the number of turns is