Discussion
The percentage error in the measurement of kinetic energy of a moving body is calculated to be 7%. If the percentage error in the measurement of mass of the body is 3%, then the percentage error in its velocity is
Answer: B
The percentage error in velocity is 2%.
For a product of powers, the relative errors add, each multiplied by its power. With K = \(\frac{1}{2}mv^{2}\):
\[ \begin{aligned} \frac{\Delta K}{K} &= \frac{\Delta m}{m} + 2\frac{\Delta v}{v} \\ 7 &= 3 + 2x \\ x &= 2\% \end{aligned} \]
4% is the result of forgetting to divide by the power 2, and 1% or 3% do not satisfy the equation.
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