Question

A simple pendulum is placed on the surface of Moon. While oscillating it rises to a maximum height of $5cm$ from its mean position. If the mass of bob is $500gram$ and acceleration due to gravity on Moon is $g=2m{s}^{-2}$. Find the below:
i) The total energy of simple pendulum at any instant while oscillating.
ii) The velocity of bob at its mean position. (Assume its mean position is at ground level)

• A. $0.5J,\sqrt{\frac{2}{5}}m{s}^{-1}$
• B. $0.05J,\sqrt{\frac{1}{5}}m{s}^{-1}$
• C. $0.05J,\sqrt{\frac{3}{5}}m{s}^{-1}$
• D. $0.5J,\sqrt{\frac{4}{5}}m{s}^{-1}$

Answer 1

The correct option is B $0.05J,\sqrt{\frac{1}{5}}m{s}^{-1}$

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