The following diagram shows a pendulum at different positions. Which o

The following diagram shows a pendulum at different positions. Which one of the following statement is true ?
[Image of a pendulum at positions P, Q, R, S, T]

[amp_mcq option1=”The pendulum has minimum potential energy at positions P and T.” option2=”The pendulum has minimum potential energy at positions Q and S.” option3=”The pendulum has minimum potential energy at position R.” option4=”The pendulum has same potential energy at all positions.” correct=”option3″]

This question was previously asked in

UPSC CDS-2 – 2023

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In a simple pendulum, potential energy is related to its height above a reference point. The lowest point in the swing represents the minimum height, and therefore, the minimum potential energy. In the diagram, position R is the lowest point of the pendulum’s swing.

Potential energy is given by PE = mgh, where m is mass, g is acceleration due to gravity, and h is height. As the pendulum swings, its height above the equilibrium position (lowest point) changes. Potential energy is maximum at the extreme positions (P and T), where the pendulum is momentarily at its highest point and stops before changing direction. Potential energy is minimum at the mean position (R), where the pendulum is at its lowest point and moving with maximum speed.

At the extreme positions (P and T), the kinetic energy is minimum (zero) because the velocity is zero. At the mean position (R), the kinetic energy is maximum because the velocity is maximum. In the absence of air resistance and friction, the total mechanical energy (sum of potential and kinetic energy) of the pendulum remains conserved throughout its swing.

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