What is the smallest radius of an unbanked (flat) track around which a bicyclist can move if her speed is $29\mathrm{ }\mathrm{k}\mathrm{m}/\mathrm{h}$ and the ${\mu }_s$ between tyres and track is $0.32?$

Given:

$$\begin{gathered} v=29\mathrm{ }\mathrm{k}\mathrm{m}/\mathrm{hr}=29\times \frac{1000}{3600}=8.1{\mathrm{ }\mathrm{m}\mathrm{s}}^{-1} \\ {\mu }_{\mathrm{s}}=0.32 \end{gathered}$$

The minimum radius of an unbanked track around which a bicyclist can move is given by the formula:

$$\begin{gathered} R_{\min }=\frac{v^2}{{\mu }_{s}g} \\ =\frac{8.1^2}{0.32\times 10} \\ =21 \mathrm{m} \end{gathered}$$

Therefore, the minimum radius of an unbanked track around which a bicyclist can move is $21m$ .

So option 1 is correct.