First, let's calculate the centripetal acceleration experienced by the monkey while the man does cycling smoothly on a circular track. The formula for centripetal acceleration ($a_c$) is given by:

$a_c = \frac{v^2}{r}$

where

• $v$ is the velocity of the monkey and the man cycling,


• $r$ is the radius of the circular track.

To find $v$, we first need to find the circumference of the circle, which is given by:

$C = 2\pi r$

Given the radius $r = 9 \, \mathrm{m}$, the circumference $C$ is:

$C = 2\pi \times 9 = 18\pi \, \mathrm{m}$

Then, we determine the total distance travelled by calculating how many times they complete the circle in the given time. With 120 revolutions in 3 minutes (180 seconds), the total distance $D$ travelled is:

$D = 120 \times C = 120 \times 18\pi = 2160\pi \, \mathrm{m}$

To find the speed $v$, which is distance over time, we divide the total distance by the total time in seconds:

$v = \frac{D}{t} = \frac{2160\pi}{180} = 12\pi \, \mathrm{m/s}$

Now, using the formula for centripetal acceleration $a_c = \frac{v^2}{r}$, we can plug in the values:

$a_c = \frac{(12\pi)^2}{9} = \frac{144\pi^2}{9} = 16\pi^2 \mathrm{~m/s}^2$

Therefore, the magnitude of the centripetal acceleration of the monkey is $16\pi^2 \, \mathrm{m/s}^2$, which corresponds to Option B.