question_answer

A cyclist is travelling with velocity v on a banked curved road of radius R. The angle 0 through which the cyclist leans inwards is given by

A) \[\tan \theta =\frac{Rg}{{{v}^{2}}}\]                       

B) \[\tan \theta ={{v}^{2}}Rg\]

C) \[\tan \theta =\frac{{{v}^{2}}g}{R}\]                       

D) \[\tan \theta =\frac{{{v}^{2}}}{Rg}\]

Correct Answer: D

Solution :

                 \[R\,cos\theta =mg\]                            ...(i)                 \[R\sin \theta =\frac{m{{v}^{2}}}{R}\]                  ...(ii) From Eqs. (i) and (ii), we get \[\therefore \]  \[\tan \theta =\frac{{{v}^{2}}}{Rg}\]