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A child is sitting on a swing which performs S.H.M. It has minimum and maximum heights from ground $0.75 \mathrm{~cm}$ and $2 \mathrm{~m}$ respectively. Its maximum speed will be $\left[\mathrm{g}=10 \frac{\mathrm{m}}{\mathrm{s}^2}\right]$
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Verified Answer
The correct answer is:
$5 \mathrm{~m} / \mathrm{s}$
Maximum potential energy is attained at the highest point which gets converted into kinetic energy at the lowest point.
$$
\begin{aligned}
& \mathrm{h}=2-0.75=1.25 \mathrm{~m} \\
& \frac{1}{2} \mathrm{mv}^2=\mathrm{mgh} \\
& \therefore \mathrm{v}^2=2 \mathrm{gh}=2 \times 10 \times 1.25=25 \\
& \therefore \mathrm{v}=5 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$
$$
\begin{aligned}
& \mathrm{h}=2-0.75=1.25 \mathrm{~m} \\
& \frac{1}{2} \mathrm{mv}^2=\mathrm{mgh} \\
& \therefore \mathrm{v}^2=2 \mathrm{gh}=2 \times 10 \times 1.25=25 \\
& \therefore \mathrm{v}=5 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$
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