What is the velocity of the bob of a simple pendulum at its...

What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of $18 \mathrm{~cm}$ (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ ) (A) $0.4 \mathrm{~m} / \mathrm{s}$ (B) $4 \mathrm{~m} / \mathrm{s}$ (C) $1.8 \mathrm{~m} / \mathrm{s}$ (D) $0.6 \mathrm{~m} / \mathrm{s}$

What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of $18 \mathrm{~cm}$ (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(A) $0.4 \mathrm{~m} / \mathrm{s}$
(B) $4 \mathrm{~m} / \mathrm{s}$
(C) $1.8 \mathrm{~m} / \mathrm{s}$
(D) $0.6 \mathrm{~m} / \mathrm{s}$

Key Concepts

Conservation of Energy

This fundamental principle of physics states that energy cannot be created or destroyed but can only be transformed from one form to another. In the context of a pendulum, the gravitational potential energy at its highest point is completely converted into kinetic energy at its lowest or mean position, neglecting air resistance and friction.

Gravitational Potential Energy

Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field. For a pendulum, this energy is at its maximum when the bob is at its highest point and zero at the lowest point, provided that the lowest point is taken as the reference level.

Kinetic Energy

Kinetic energy is the energy of motion. When a pendulum bob swings down from its highest point, the potential energy it lost is converted into kinetic energy, reaching a maximum value at the mean position. This energy conversion is directly used to calculate the velocity of the bob.

Simple Pendulum Dynamics

The simple pendulum model assumes a point mass suspended by a weightless, inextensible string and undergoing oscillations under the influence of gravity. Understanding its dynamics involves analyzing the energy transformations between potential and kinetic states, primarily using the conservation of energy to relate the vertical displacement to the velocity at different points in the swing.

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