Question

A cyclist is moving in a circular track of radius $ 80\, m $ with a velocity $ v\, =\, 36 \, km/h $ . He has to lean from the vertical approximately through an angle: (Take $ g=10\text{ }m{{s}^{-2}}) $

• A. $ {{\tan }^{-1}}(4) $
• B. $ {{\tan }^{-1}}\left( \frac{1}{3} \right) $
• C. $ {{\tan }^{-1}}\left( \frac{1}{4} \right) $
• D. $ {{\tan }^{-1}}(2) $
• E. $ {{\tan }^{-1}}\left( \frac{1}{8} \right) $

Answer 1

Answer: (E)

$ \tan \theta =\frac{{{v}^{2}}}{rg} $
$ \Rightarrow $ $ \theta ={{\tan }^{-1}}\left( \frac{10\times 10}{80\times 10} \right) $
$ \left( \because v=36\times \frac{5}{18}=10\,m/s \right) $
$ ={{\tan }^{-1}}\left( \frac{1}{8} \right) $