Write the formula for the maximum permissible speed of a vehicle moving on a smooth banked circular track.

(N/A) The velocity of a vehicle on a banked circular road is given by the general formula:
$v = \left[ rg \left( \frac{\mu_s + \tan \theta}{1 - \mu_s \tan \theta} \right) \right]^{1/2}$
For a smooth surface,the coefficient of static friction $\mu_s = 0$.
Substituting $\mu_s = 0$ into the formula:
$v_{\max} = \left[ rg \left( \frac{0 + \tan \theta}{1 - 0 \cdot \tan \theta} \right) \right]^{1/2}$
$v_{\max} = \left[ rg \tan \theta \right]^{1/2}$
Therefore,the formula for the maximum permissible speed on a smooth banked track is:
$v_{\max} = \sqrt{rg \tan \theta}$
At this speed,the horizontal component of the normal force provides the necessary centripetal force,and no frictional force is required.