Physics Work & Energy UHS 2023
PMDC Verified Question 21 of 108
Two bodies with kinetic energies in the ratio of 4:1 are moving with equal linear momentum. The ratio of their masses is:
A
1:2
B
1:1
C
4:1
D
1:4
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: 1:4
Concept:

Use the algebraic relationship linking Kinetic Energy, Momentum, and Mass.

Formula:

$$ K.E = \frac{p^2}{2m} $$

Solution:

  • Since momentum (\( p \)) is equal for both bodies, \( K.E \) is inversely proportional to mass (\( K.E \propto \frac{1}{m} \)).


  • Therefore, \( \frac{K.E_1}{K.E_2} = \frac{m_2}{m_1} \).


  • Given \( \frac{K.E_1}{K.E_2} = \frac{4}{1} \), it follows that \( \frac{m_2}{m_1} = \frac{4}{1} \).


  • Inverting this to find the ratio of their masses (\( m_1:m_2 \)): \( \frac{m_1}{m_2} = \frac{1}{4} \).


  • So, the ratio is 1:4.


Why other options are incorrect:

Assuming direct proportionality yields 4:1. Forgetting to square a velocity term if using \( 1/2mv^2 \) leads to 1:2.

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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