The increase in periodic time of a simple pendulum executing...

The increase in periodic time of a simple pendulum executing S.H.M. is $\ldots \ldots \ldots \ldots \ldots \ldots$ when its length is increased by $21 \%$.
(A) $42 \%$
(B) $10 \%$
(C) $11 \%$
(D) $21 \%$.

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Key Concepts

Simple Pendulum

A simple pendulum consists of a mass suspended from a fixed point such that it can swing freely under the influence of gravity. It is an idealized system used to study periodic motion and is characterized by exhibiting simple harmonic motion when the oscillations are small.

Pendulum Period Formula

The period of a simple pendulum is given by T = 2??(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. This formula shows that the period depends on the square root of the pendulum's length.

Square Root Dependence and Percentage Changes

Since the period of a pendulum is proportional to the square root of its length, any percentage increase in the length results in a smaller percentage increase in the period. Specifically, a percentage change in length is reduced by the square root factor, meaning that increasing the length by a given percentage increases the period by approximately half that percentage for small changes.

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