Question

The percentage error in the measurement of mass and speed of a particular body is 3% and 4% respectively. The percentage error in the measurement of kinetic energy is

• A. 9%
• B. 10%
• C. 11%
• D. 12%

Hint:

In power functions $y = x^n$, the relative error is $n$ times the relative error in $x$.

Answer 1

The Correct Option is C

Step 1: Formula
Kinetic Energy ($K.E.$) $= \frac{1}{2}mv^2$.
Step 2: Error Analysis
For $K.E. = \frac{1}{2}mv^2$, the maximum relative error is given by:
$\frac{\Delta K.E.{K.E. \times 100 = \left( \frac{\Delta m}{m} \times 100 \right) + 2 \left( \frac{\Delta v}{v} \times 100 \right)$.
Step 3: Calculation
$% \text{ Error in } K.E. = 3% + 2(4%) = 3% + 8% = 11%$.
Final Answer: (C)