Physics Waves NUMS 2022
PMDC Verified Question 71 of 125
If the period of oscillation of mass (M) suspended from a spring is 1s, then the period of 16M will be:
A
1s
B
2s
C
3s
D
4s
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: 4s
Concept:

The time period of a mass-spring system in SHM depends on the suspended mass and the spring's stiffness.

Formula:

$$ T = 2\pi \sqrt{\frac{m}{k}} $$

Solution:

  • The original period is \( T_1 = 1 \text{ s} \), which is proportional to \( \sqrt{M} \).


  • The mass is increased to \( 16M \). The new period \( T_2 \) is proportional to \( \sqrt{16M} \).


  • Extract the constant from the square root: \( \sqrt{16M} = 4\sqrt{M} \).


  • Therefore, the new period is exactly 4 times the original period: \( T_2 = 4 \times 1 \text{ s} = 4 \text{ s} \).


Why other options are incorrect:

If a student assumes period scales linearly with mass (rather than the square root), they would erroneously look for 16s. A student might also divide instead of multiply.

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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