Question

What is the smallest radius of a circular path on which a cyclist can travel with uniform speed of $36km{h}^{-1}$, with angle of inclination (from vertical, for cyclist) ${45}^{\circ }$ and $g=10m{s}^{-2}$ ?

• A. $20\text{m}$
• B. $10\text{m}$
• C. $30\text{m}$
• D. $40\text{m}$

Answer 1

The correct option is B $10\text{m}$

The components of Normal reaction for cyclist need to satisfy the equation of dynamics i.e. supporting the weight & centripetal force.

So, we have
$N\sin \theta =\frac{m{v}^2}{r}$.......(i)
$N\cos \theta =mg$..........(ii)
On dividing (i) by (ii), we get
$\tan \theta =\frac{v^2}{rg}$
$\Rightarrow r=\frac{v^2}{g\tan \theta }=\frac{10\times 10}{10\times \tan {45}^{\circ }}=10\text{m}$