Physics Work & Energy NUMS 2024
PMDC Verified Question 14 of 108
The relation between K.E and momentum P is given by:
A
\( K.E = \frac{P}{2m} \)
B
\( K.E = \frac{P}{2m^2} \)
C
\( K.E = \frac{P^2}{2m} \)
D
\( K.E = \frac{P^2}{2m^2} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( K.E = \frac{P^2}{2m} \)
Concept:

This requires algebraic substitution of the momentum equation into the kinetic energy equation.

Formula:

$$ p = mv \quad \text{and} \quad K.E = \frac{1}{2}mv^2 $$

Solution:

  • From \( p = mv \), isolate \( v \): \( v = \frac{p}{m} \).


  • Substitute this \( v \) into the K.E equation: \( K.E = \frac{1}{2}m\left(\frac{p}{m}\right)^2 \).


  • Expand the square: \( K.E = \frac{1}{2}m \left(\frac{p^2}{m^2}\right) \).


  • Cancel one mass term (\( m \)) from the numerator and denominator: \( K.E = \frac{p^2}{2m} \).


Why other options are incorrect:

Option A forgets to square the momentum. Options B and D incorrectly square the mass in the denominator.

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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