Question

A circular road of radius 50 m has the angle of banking equal to 30^{\circ}. At what speed should a vehicle go on this road so that the friction is not used ?

Answer 1

Angle of banking = $\theta ={30}^{\circ }$

Radius = r = 50 m

$tan\theta =\left(\frac{v^2}{rg}\right)tan{30}^{\circ }\Rightarrow \left(\frac{1}{\sqrt{3}}\right)=\left(\frac{v^2}{rg}\right)\Rightarrow v^2=\frac{rg}{\sqrt{3}}=\frac{50\times 10}{\sqrt{3}}\Rightarrow v=\sqrt{\frac{500}{\sqrt{3}}}=17m/sec$