Chapter P4, Problem 1MCPE

To determine

How would the time for to and fro motion over a playground swing vary if instead of sitting we stand on the swing?

Answer to Problem 1MCPE

Solution: Option (b) Shortened

Explanation of Solution

Swinging can be compared with the motion of a simple pendulum.
The time is taken for a pendulum swinging to and fro is called its period denoted by T.
The period of a simple pendulum is given by:
$\begin{array}{l}T=2\pi \sqrt{\frac{l}{g}}\\ \end{array}$
$l\to$ Length of the pendulum
$g\to$ Acceleration due to gravity
So, the period depends only on the length of the pendulum. When standing on the playground swing, our center of mass shifts closer to the pivot and hence, effective length decreases which decreases the period for the swing.

Conclusion:

The period for to and fro motion on a playground swing is shortened if we stand on it instead of sitting.