Question

20. A pendulum bob of mass m kg is raised up to a height h m and then
released. What is the velocity of the bob, when it reaches mean position.
a. V = V √2gh
b. v = 2gh
C. V = gh/2
d. v = √gh/2​

Answer 1

Given:

A pendulum bob of mass m kg is raised up to a height h m and then released.

To find:

What is the velocity of the bob, when it reaches mean position ?

Calculation:

In these kind of questions, you need to apply CONSERVATION OF MECHANICAL ENERGY, where the potential energy of the bob (at height h) will be fully converted to to the kinetic energy (at the mean position).

• The mean position of the pendulum will be considered as the reference plane, potential energy will be considered zero.

$\rm \therefore \: - \Delta PE = \Delta KE$

$\rm \implies \: - (0 - mgh) = \dfrac{1}{2} m {v}^{2} - 0$

$\rm \implies \: \dfrac{1}{2} m {v}^{2} = mgh$

$\rm \implies \: \dfrac{1}{2} {v}^{2} = gh$

$\rm \implies \: {v}^{2} = 2gh$

$\rm \implies \: v = \sqrt{ 2gh}$

So, Velocity of bob at mean position is √(2gh) .