Question 47: Work, Energy and Power & Circular Motion

Question

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $$9 \mathrm{~m}$$ and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $$\mathrm{m} / \mathrm{s}^2$$ ) :

Accepted Answer

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:
$C = 2\pi 	imes 9 = 18\pi \, \mathrm{m}$
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:
$D = 120 	imes C = 120 	imes 18\pi = 2160\pi \, \mathrm{m}$
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.

Answer

$$4 \pi^2 \mathrm{~ms}^{-2}$$

Answer

$$16 \pi^2 \mathrm{~ms}^{-2}$$

Answer

$$57600 \pi^2 \mathrm{~ms}^{-2}$$

Answer

Zero

Work, Energy and Power & Circular Motion

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $9 \mathrm{~m} and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in \mathrm{m} / \mathrm{s}^2$ ) :

Choose the correct answer: