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
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
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In error propagation, powers are multiplied by the relative error of the base.
Updated On: Apr 30, 2026
- 1%
- 2%
- 6%
- 8%
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The Correct Option is D
Solution and Explanation
Step 1: Formula
Pressure $P = \frac{F}{A} = \frac{F}{L^2}$
Step 2: Error Analysis
$\frac{\Delta P}{P} \times 100 = \left( \frac{\Delta F}{F} + 2 \frac{\Delta L}{L} \right) \times 100$
Step 3: Calculation
$% \text{ error in } P = 4% + 2(2%)$
$% \text{ error in } P = 4% + 4% = 8%$
Step 4: Conclusion
The total percentage error is 8%.
Final Answer:(D)
Pressure $P = \frac{F}{A} = \frac{F}{L^2}$
Step 2: Error Analysis
$\frac{\Delta P}{P} \times 100 = \left( \frac{\Delta F}{F} + 2 \frac{\Delta L}{L} \right) \times 100$
Step 3: Calculation
$% \text{ error in } P = 4% + 2(2%)$
$% \text{ error in } P = 4% + 4% = 8%$
Step 4: Conclusion
The total percentage error is 8%.
Final Answer:(D)
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