Question

A pendulum attached with a string of length 2 m is released from one of its extreme
position at an angle of 30° from the vertical. What will be its velocity when it passes the mean
position? Take ‘g'as 10 m/s?.​

Answer 1

Given :

Length of the pendulum = 2m

It is released from one of its extreme position at an angle of 30° from the vertical.

To Find :

Velocity of pendulum when it passes the mean position.

Solution :

❖ Let potential energy at mean position be zero.

This question can be easily solved by concept of energy conservation.

• Potential energy at extreme position will be equal to the kinetic energy at mean position.

$\sf:\implies\:(KE)_{mean}=(PE)_{extreme}$

$\sf:\implies\:\dfrac{1}{2}mv^2=mgH$

$\sf:\implies\:v^2=2gH$

$\sf:\implies\:v^2=2g\:(L-Lcos30^{\circ})$

$\sf:\implies\:v^2=2\times10\times 2\:\left(1-\dfrac{\sqrt3}{2}\right)$

$\sf:\implies\:v^2=40\:\left(\dfrac{2-1.73}{2}\right)$

$\sf:\implies\:v^2=40\times\dfrac{0.27}{2}$

$\sf:\implies\:v=\sqrt{5.4}$

$:\implies\:\underline{\boxed{\bf{\gray{v=2.32\:ms^{-1}}}}}$