Question:
The percentage error in the measurement of mass and velocity are 3% and 4% respectively. The percentage error in the measurement of kinetic energy is:
The percentage error in the measurement of mass and velocity are 3% and 4% respectively. The percentage error in the measurement of kinetic energy is:
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For error propagation in multiplication, sum the relative errors. For exponentiation, multiply the relative error by the exponent.
Updated On: Jun 18, 2025
- \( 11\% \)
- \( 12\% \)
- \( 14\% \)
- \( 8\% \)
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The Correct Option is A
Solution and Explanation
Step 1: Define the Kinetic Energy Formula
Kinetic energy is given by:
\[
KE = \frac{1}{2} m v^2
\]
Taking the logarithm on both sides:
\[
\log KE = \log \left( \frac{1}{2} \right) + \log m + 2 \log v
\]
Differentiating both sides:
\[
\frac{d(KE)}{KE} = \frac{dm}{m} + 2 \frac{dv}{v}
\]
Step 2: Calculate the Percentage Error
The percentage error in \( m \) is given as \( 3\% \) and in \( v \) as \( 4\% \). Using the formula:
\[
\% \text{ Error in } KE = \% \text{ Error in } m + 2 \times \% \text{ Error in } v
\]
\[
= 3\% + 2(4\%) = 3\% + 8\% = 11\%
\]
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