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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

The kinetic energy of a particle is determined by measuring its...

The kinetic energy of a particle is determined by measuring its momentum and mass. If the maximum percentage errors in the measurement of momentum and mass are 4%4\% and 3%3\% respectively, then the maximum percentage error in the calculated value of kinetic energy will be:

Options

  1. A55
  2. B77
  3. C1010
  4. D1111

Correct answer

D. 1111

Step-by-step solution

The kinetic energy KK of a particle is related to its momentum pp and mass mm by the relation:
K=p22mK = \dfrac{p^2}{2m}

The maximum percentage error in kinetic energy is given by:
ΔKK×100=2(Δpp×100)+Δmm×100\dfrac{\Delta K}{K} \times 100 = 2 \left( \dfrac{\Delta p}{p} \times 100 \right) + \dfrac{\Delta m}{m} \times 100

Given that the percentage errors in momentum and mass are 4%4\% and 3%3\% respectively:
ΔKK×100=2(4%)+3%=8%+3%=11%\dfrac{\Delta K}{K} \times 100 = 2(4\%) + 3\% = 8\% + 3\% = 11\%

Answer: 1111
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