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MHT CET 202621 AprilEvening Shift

Exam: MHT CET
Year: 2026
Date: 21 April
Shift: Evening Shift
Subject: Physics
Chapter: Oscillations

MHT CET 2026 · 21 April · Evening Shift · Physics · Oscillations

If the kinetic energy of simple pendulum is (1)/(4) of its total...

If the kinetic energy of simple pendulum is

\dfrac{1}{4}

of its total energy, then the displacement (

x

) and amplitude (

A

) are related as

Options

A $x = A$
B $x = 2A$
C $x = \dfrac{\sqrt{3}}{2}A$
D $x = \dfrac{\sqrt{3}}{4}A$

Correct answer

C. $x = \dfrac{\sqrt{3}}{2}A$

Step-by-step solution

Total energy of a simple pendulum executing SHM is given by

E = \dfrac{1}{2} m \omega^2 A^2

Kinetic energy at displacement

x

is given by

K = \dfrac{1}{2} m \omega^2 (A^2 - x^2)

Given that

K = \dfrac{1}{4} E

\dfrac{1}{2} m \omega^2 (A^2 - x^2) = \dfrac{1}{4} \left( \dfrac{1}{2} m \omega^2 A^2 \right)

A^2 - x^2 = \dfrac{A^2}{4}

x^2 = A^2 - \dfrac{A^2}{4} = \dfrac{3A^2}{4}

x = \dfrac{\sqrt{3}}{2} A

Answer:

x = \dfrac{\sqrt{3}}{2}A

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