Question

A child is sitting on a swing whose minimum and maximum heights from the ground are $0.75\text{m}$ and $2\text{m}$ respectively. Its maximum speed will be

• A. $10\text{m/s}$
• B. $5\text{m/s}$
• C. $8\text{m/s}$
• D. $15\text{m/s}$

Answer 1

The correct option is B $5\text{m/s}$

The point where the potential energy is minimum, i.e, the point of minimum height from the ground, the kinetic energy is maximum and hence the speed will be maximum.
Also at the point where the height is maximum the potential energy will also be maximum and kinetic energy will be 0.
According to the conservation of mechanical energy,
Loss in PE = Gain in KE
$\therefore mg(2-0.75)=\frac{1}{2}m{v}_{max}^2$
$\Rightarrow v_{max}=\sqrt{2g\left(1.25\right)}=5\text{m/s}$
Hence, the correct answer is option (b).