Question

The pressure on a square plate is measured by measuring the force acting on the plate and length of the sides of the plate. The maximum error in the measurement of force and length are respectively 4% and 2%, the percentage error in the measurement of pressure is

• A. 1%
• B. 2%
• C. 6%
• D. 8%

Hint:

In error propagation, powers are multiplied by the relative error of the base.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to calculate the propagated error in a derived quantity (pressure) from measured quantities (force and length).
Step 2: Key Formula or Approach:
Pressure \( P = \frac{F}{A} = \frac{F}{L^2} \).
Relative error: \( \frac{\Delta P}{P} = \frac{\Delta F}{F} + 2 \frac{\Delta L}{L} \).
Step 3: Detailed Explanation:
Given percentage errors:
\( \frac{\Delta F}{F} \times 100 = 4% \)
\( \frac{\Delta L}{L} \times 100 = 2% \)
The percentage error in pressure is:
\[ \text{% error in P} = \left( \frac{\Delta F}{F} + 2 \frac{\Delta L}{L} \right) \times 100 \] \[ = 4% + 2(2%) = 4% + 4% = 8% \] Step 4: Final Answer:
The percentage error in measurement of pressure is 8%.