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: Understanding the Concept:
Kinetic energy of a body depends on its mass and the square of its speed. When calculating the error in a derived quantity, the relative errors of the constituent quantities are added, weighted by the powers to which they are raised.
Step 2: Key Formula or Approach:
The formula for Kinetic Energy is:
\[ K = \frac{1}{2}mv^2 \]
The percentage error in Kinetic Energy (\(K\)) is given by:
\[ \left( \frac{\Delta K}{K} \times 100 \right) = \left( \frac{\Delta m}{m} \times 100 \right) + 2 \times \left( \frac{\Delta v}{v} \times 100 \right) \]
Step 3: Detailed Explanation:
Given values:
Percentage error in mass, \(\frac{\Delta m}{m} \times 100 = 3%\)
Percentage error in speed, \(\frac{\Delta v}{v} \times 100 = 4%\)
Substituting these values into the error formula:
\[ % \text{ error in } K = 3% + 2 \times (4%) \]
\[ % \text{ error in } K = 3% + 8% \]
\[ % \text{ error in } K = 11% \]
Step 4: Final Answer:
The percentage error in the measurement of kinetic energy is 11%.