Assertion : When percentage errors in the measurement of mass and velocity are $1\%$ and $2\%$ respectively, the percentage error in $K.E.$ is $5\%$.
Reason : $\frac{{\Delta E}}{E} = \frac{{\Delta m}}{m} + \frac{{2\Delta v}}{v}$
Reason : $\frac{{\Delta E}}{E} = \frac{{\Delta m}}{m} + \frac{{2\Delta v}}{v}$
AIIMS 2010, Easy
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Both Assertion and Reason correct and Reason is the correct explanation of Assertion.
Kinetic energy, $E=\frac{1}{2} m v^2$
Differenting both side
$\frac{\Delta E}{E}=\frac{\Delta m}{m}+\frac{2 \Delta v}{v}$
$\frac{\Delta E}{E}=\frac{1}{100}+2 \times \frac{2}{100}=\frac{5}{100}=5 \%$
Kinetic energy, $E=\frac{1}{2} m v^2$
Differenting both side
$\frac{\Delta E}{E}=\frac{\Delta m}{m}+\frac{2 \Delta v}{v}$
$\frac{\Delta E}{E}=\frac{1}{100}+2 \times \frac{2}{100}=\frac{5}{100}=5 \%$
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