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  4. A child swinging on a swing m a sitting position, stands up, then the time period of the swing will:

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Q. A child swinging on a swing $m$ a sitting position, stands up, then the time period of the swing will:

Delhi UMET/DPMTDelhi UMET/DPMT 2004

Solution:

When child stands up centre of mass shifts upwards.
The child swings in simple harmonic motion,
hence time-period is given by
$T=2 \pi \sqrt{\frac{l}{g}}$
$\Rightarrow T \propto \sqrt{l}$
where $ l $ is length of swing.
When child stands up,
the length is shortened as centre of mass shifts up,
hence time period decreases.