Question

A child is swinging a swing. Minimum and maximum heights of swing from earths surface are $0.75 \,m$ and $2\,m$ respectively. The maximum velocity of this swing is:

• A. 5 m/s
• B. 10 m/s
• C. 15 m/s
• D. 20 m/s

Answer 1

Answer: (A)

Maximum kinetic energy of swing should be equal to difference in potential energies to conserve energy.
From energy conservation
$\frac{1}{2} m v_{\max }^{2}=m g\left(H_{2}-H_{1}\right)$
Here, $H _{1}=$ maximum height of swing from earths surface
$=0.75 \,m $
$H _{2}=$ maximum height of swing from earths surface $=2\, m$
$\therefore \frac{1}{2} m v_{\max }^{2}=m g(2-0.75)$
or $v_{\max }=\sqrt{2 \times 10 \times 1.25}$
$=\sqrt{25}=5\, m / s$