Physics Waves UHS 2022
PMDC Verified Question 62 of 125
Reducing mass M of a suspending body to one fourth will change the frequency of oscillations be:
A
One fourth
B
Double
C
Quadrupled
D
Half
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: Double
Concept:

The frequency of a mass-spring system in Simple Harmonic Motion depends inversely on the square root of its mass.

Formula:

$$ f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} $$

Solution:

  • The original frequency is \( f \propto \frac{1}{\sqrt{m}} \).


  • The mass is reduced to one-fourth: \( m_{new} = \frac{m}{4} \).


  • Substitute this new mass into the proportionality: \( f_{new} \propto \frac{1}{\sqrt{m/4}} \).


  • Simplify the square root: \( \frac{1}{\sqrt{m}/2} = 2 \times \frac{1}{\sqrt{m}} \).


  • Therefore, the new frequency is exactly double the original frequency (\( f_{new} = 2f \)).


Why other options are incorrect:

Reducing mass increases frequency (it oscillates faster). Option C (quadruple) comes from forgetting to take the square root of 4.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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