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:

• A. \( 11\% \)
• B. \( 12\% \)
• C. \( 14\% \)
• D. \( 8\% \)

Hint:

For error propagation in multiplication, sum the relative errors. For exponentiation, multiply the relative error by the exponent.

Answer 1

The Correct Option is A

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: \[ \% \text{ Error in } KE = \% \text{ Error in } m + 2 \times \% \text{ Error in } v \] \[ = 3\% + 2(4\%) = 3\% + 8\% = 11\% \]