Question

The percentage errors in measurements of mass and speed of a body are 2% and 3% respectively. What is the percentage error in kinetic energy of the body?

• A. 9%
• B. 5%
• C. 8%
• D. 0%

Hint:

For quantities involving powers, multiply the percentage error by the power of the variable.

Answer 1

The Correct Option is C

Step 1: Expression for kinetic energy.
Kinetic energy is given by \[ K = \frac{1}{2}mv^2. \]
Step 2: Applying error propagation.
For a quantity of the form \(K \propto m v^2\), the percentage error is \[ \frac{\Delta K}{K} = \frac{\Delta m}{m} + 2\frac{\Delta v}{v}. \]
Step 3: Substituting given values.
\[ \frac{\Delta K}{K} = 2% + 2(3%) = 2% + 6% = 8%. \]
Step 4: Conclusion.
The percentage error in kinetic energy is 8%.