Question

The bob of a simple pendulum of thread length $l$ is pulled aside and held in level with the point of suspension O as shown in the figure and then released. Determine the speed of the bob when it passes through its lowest point. Consider the thread to be perfectly inelastic and almost inextensible.

Answer 1

The speed of the bob when it passes through its lowest point is $\sqrt{2gl}$.

Answer 2

The bob is released from rest at a height $l$ above its lowest point. By conservation of mechanical energy, the initial potential energy ($mgl$) is converted entirely into kinetic energy ($\frac{1}{2}mv^2$) at the lowest point. Equating these yields $mgl = \frac{1}{2}mv^2$, which simplifies to $v = \sqrt{2gl}$.