question_answer

A cyclist is travelling with velocity v on a banked curved road of radius R. The angle \[\theta \] 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 \[\therefore \] \[\tan \theta =\frac{{{v}^{2}}}{Rg}\]