Question

What is the smallest radius of a circle in which a cyclist can travel if its speed is 108 km/h, angle of inclination 370 and g=10m/s2 ?

Answer 1

Cyclists wants to travel at 108 km/hr. Angle of banking of road is 37° and g = 10 m/s². Let radius of road be r :

• 108 km/hr = 108 × 5/18 = 30 m/s.

• The general expression for banking of road (excluding friction consideration) is as follows:

$\tan( \theta) = \dfrac{ {v}^{2} }{rg}$

$\implies \tan( {37}^{ \circ} ) = \dfrac{ {30}^{2} }{r \times 10}$

$\implies \dfrac{3}{4} = \dfrac{900}{r \times 10}$

$\implies \dfrac{3}{4} = \dfrac{90}{r }$

$\implies r = 120 \: metres$

So, radius of banked road is 120 metres.