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JEE Main 202122 JulyMorning Shift

Exam: JEE Main
Year: 2021
Date: 22 July
Shift: Morning Shift
Subject: Physics
Chapter: Oscillations

JEE Main 2021 · 22 July · Morning Shift · Physics · Oscillations

T _ 0 is the time period of a simple pendulum at a place. If the...

{T}_{0}

is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to

\dfrac{1}{16}

times of its initial value, the modified time period is

Options

A ${T}_{0}$
B $8\pi{T}_{0}$
C $4{T}_{0}$
D $\dfrac{1}{4}{T}_{0}$

Correct answer

D. $\dfrac{1}{4}{T}_{0}$

Step-by-step solution

{T}_{0} = 2\pi\sqrt{\dfrac{ℓ}{g}}

New time period,

T = = 2\pi\sqrt{\dfrac{\left(\dfrac{ℓ}{16}\right)}{g}} = \dfrac{2\pi}{4}\sqrt{\dfrac{ℓ}{g}}

T = \dfrac{{T}_{0}}{4}

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