A child is sitting on a swing which performs S.H.M. It has minimum and maximum heights from ground $0.75…

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 $\left[\mathrm{g}=10 \frac{\mathrm{m}}{\mathrm{s}^2}\right]$
  1. $\sqrt{1.25} \mathrm{~m} / \mathrm{s}$
  2. $\sqrt{12.5} \mathrm{~m} / \mathrm{s}$
  3. $5 \mathrm{~m} / \mathrm{s}$
  4. $25 \mathrm{~m} / \mathrm{s}$

Solution

Maximum potential energy is attained at the highest point which gets converted into kinetic energy at the lowest point. $\begin{aligned} & \mathrm{h}=2-0.75=1.25 \mathrm{~m} \\ & \frac{1}{2} \mathrm{mv}^2=\mathrm{mgh} \\ & \therefore \mathrm{v}^2=2 \mathrm{gh}=2 \times 10 \times 1.25=25 \\ & \therefore \mathrm{v}=5 \mathrm{~m} / \mathrm{s} \end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

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