**Solution**. We know that for a body moving in a circular path :

Here,

$$

v=\frac{2 \pi r}{t}

$$

$$

\begin{aligned}

\text { Speed, } v &=? \\

\mathrm{pi}, \pi &=\frac{22}{7}

\end{aligned}

$$

(To be calculated)

Radius of circular track, $r=105 \mathrm{~m}$

And, Time taken for 1 round, $t=2$ minutes

$$

\begin{array}{l}

=2 \times 60 \text { seconds } \\

=120 \mathrm{~s} .

\end{array}

$$

Now, putting these values of $\pi, r$ and $t$ in the above formula, we get :

$$

\begin{aligned}

v &=\frac{2 \times 22 \times 105}{7 \times 120} \\

&=5.5 \mathrm{~m} / \mathrm{s}

\end{aligned}

$$

Thus, the speed of cyclist on the circular track is $5.5$ metres per second.