Question

A simple pendulum, while oscillating rises to a maximum vertical height of $5cm$ from its rest position. Assume its rest position is at ground level. If the mass of bob of the simple pendulum is $500g$ and acceleration due to gravity g = $10m/s^2$. Find the below:
i) The total energy of simple pendulum at any instant while oscillating.
ii) The velocity of bob at its resting position.

• A. 0.25 J,1 m/s
• B. 0.25 J,5 m/s
• C. 0.30 J,5 m/s
• D. 0.30 J,1 m/s

Answer 1

The correct option is A

0.25 J,1 m/s

Given,
Mass $m=500g=0.5kg$
Height $h"=5cm$ = $0.05m$
Assuming there is no loss in energy due to air friction,
(i) Total energy of simple pendulum
= Potential energy at its extreme position
= $mgh$ = $0.5\times 10\times 0.05$ = $0.25J$
(ii) Kinetic energy at a mean position
Change in PE = Change in KE
= $\frac{1}{2}m{v}^2=mgh$
or $v=\sqrt{2gh}=\sqrt{2\times 10\times 0.05}=\sqrt{1}$
= $1m{s}^{-1}$