Kinetic Energy And Momentum Relation
Two bodies of different masses possess the same magnitude of linear momentum while moving in a straight line. Which body has the greater kinetic energy, and on what does the comparison depend?
Select the correct option:
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About This Question
- Subject
- physics
- Chapter
- work, energy and power
- Topic
- kinetic energy and momentum relation
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
The lighter body, because kinetic energy is inversely proportional to mass for fixed momentum
As stated in NCERT Class 11, Chapter 6 (Work, Energy and Power), kinetic energy can be written in terms of momentum as KE = p²/(2m), where p is the linear momentum and m is the mass. When two bodies share the same momentum magnitude, the kinetic energy varies inversely with mass, so the lighter body has the greater kinetic energy. The option favouring the heavier body misapplies the direct formula (1/2)mv² without accounting for the fixed-momentum constraint. The option claiming equal kinetic energy ignores the mass dependence entirely. The option saying it cannot be determined is wrong because the relation KE = p²/(2m) settles it directly. A consistency check: for equal p, doubling the mass halves the kinetic energy, confirming that the smaller mass carries more energy, which is the correct conclusion.
This medium difficulty physics question is from the chapter work, energy and power, covering the topic of kinetic energy and momentum relation. It appeared in the 2025 exam.
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