If the frequency of the rotating platform is f and the distance of a boy from the centre is r, which is the area swept out per second by line connecting the boy to the centre

The correct option is πr²f.

To find the area swept out per second by the line connecting the boy to the centre of the rotating platform, we can analyze the motion step-by-step:

1. When the platform makes one complete revolution, the boy moves along a circular path of radius
$r$
. The area swept out by the line connecting the boy to the centre during this single rotation is equal to the area of a circle of radius
$r$
.

The area of a circle is given by:

$A=\pi r^2$

2. The frequency
$f$
represents the number of complete revolutions the platform makes per second.

3. Therefore, the total area swept out per second is the area of a single circle multiplied by the frequency:

$\text{Area swept per second}=\pi r^{2}f$