JEE Main 2024 — Circular Motion Question with Solution

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:

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

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

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

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