A physical quantity Q is found to depend on observables x- y and z obeying relation Q-x3y2-z- The percentage error in the measurement of x- y and z are 1- 2- and 4- respectively- What is the percentage error in the quantity Q -

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Standard VIII

Physics

Accuracy and Precision

A physical qu...

Question

A physical quantity $Q$ is found to depend on observables $x, y$ and $z$ obeying relation $Q = \frac{x^{3} y^{2}}{z}$ . The percentage error in the measurement of $x, y$ and $z$ are $1 %, 2 %$ and $4 %$ respectively. What is the percentage error in the quantity $Q$ ?

$4 %$

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$3 %$

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$11 %$

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$1 %$

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Solution

The correct option is C
$11 %$

Step 1. Given data
$Q = \frac{x^{3} y^{2}}{z}$
$\frac{∆ x}{x} = 1 %$
$\frac{∆ y}{y} = 2 %$
$\frac{∆ z}{z} = 4 %$
Step 2. Finding the percentage error in $Q$
By using the percentage error formula,
$\frac{∆ Q}{Q} = 3 \times \frac{∆ x}{x} + 2 \times \frac{∆ y}{y} + \frac{∆ z}{z}$
$\frac{∆ Q}{Q} = 3 \times 1 % + 2 \times 2 % + 4 %$
$\frac{∆ Q}{Q} = 11 %$
Therefore, the percentage error in $Q$ is $11 %$ .
Hence, the correct option is $(C)$ .

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A physical quantity Q is found to depend on observables x,y and z obeying relation Q=x3y2z. The percentage error in the measurement of x,y and z are 1%,2% and 4% respectively. What is the percentage error in the quantity Q ?

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