JEE Main 2023 — Circular Motion Question with Solution

To calculate the centrifugal force acting on the child, we need to find the angular velocity of the merry-go-round and then apply the formula for centrifugal force.

The merry-go-round makes 1 rotation in 3.14 seconds, so its angular velocity ($$\omega$$) can be calculated as:

$$\omega =\frac{2\pi }{T}$$, where $$T$$ is the time period for one rotation.

$$\omega =\frac{2\pi }{3.14}=2\text{radians/s}$$

Now, the formula for centrifugal force ($$F$$) is:

$$F=m\cdot r\cdot {\omega }^2$$, where $$m$$ is the mass of the child, $$r$$ is the radius of the merry-go-round, and $$\omega$$ is the angular velocity.

$$F=5\text{kg}\cdot 2\text{m}\cdot (2\text{radians/s}{)}^2=5\text{kg}\cdot 2\text{m}\cdot 4(\text{radians/s}{)}^2$$

$$F=40\text{N}$$

Therefore, the centrifugal force on the child is $$40\text{N}$$.