Question:
The pressure on a square plate is measured by measuring the force on the plate. If the maximum error in the measurement of force and length are respectively $4\%$ and $2\%$, then the maximum error in the measurement of pressure is
The pressure on a square plate is measured by measuring the force on the plate. If the maximum error in the measurement of force and length are respectively $4\%$ and $2\%$, then the maximum error in the measurement of pressure is
Updated On: Apr 15, 2024
- 1%
- 2%
- 4%
- 8%
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The Correct Option is D
Solution and Explanation
We have,
Pressure $=\frac{\text { Force }}{\text { Area }}=\frac{F}{L^{2}}$
$\therefore \frac{\Delta p}{p}=\frac{\Delta F}{F}+\frac{2 \Delta L}{L}$
$=4 \%+2(2 \%)=8 \%$
Pressure $=\frac{\text { Force }}{\text { Area }}=\frac{F}{L^{2}}$
$\therefore \frac{\Delta p}{p}=\frac{\Delta F}{F}+\frac{2 \Delta L}{L}$
$=4 \%+2(2 \%)=8 \%$
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Concepts Used:
Partial Pressure
Partial Pressure is defined as if a container filled with more than one gas, each gas exerts pressure. The pressure of anyone gas within the container is called its partial pressure.
Dalton’s Law of Partial Pressure:
According to Dalton’s law of partial pressures, the total pressure exerted by the mixture of gases is the sum of the partial pressure of every existing individual gas, and every gas is assumed to be an Ideal gas.
Ptotal = P1 + P2 + P3 …
Where P1, P2, P3 are the partial pressures of gas 1, gas 2, and gas 3. Since every gas has an independent behavior, the ideal gas law is used to find the pressure of that gas if its number of moles, the volume of container and temperature is known.