QJEEM23Phd45b: JEE Main 2023 Physics - Class 11 JEEM23Phd45b Solution: A child of mass is going round a merry-go-round that makes 1…

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 $40\,\text{N}$ .