If P=[(A^2 B) /(C^3)] where percentage error in A, B and C are respectively ±2 % ±3 % and ±5 %

step 1 Okay in this question if if p equal to a square b out of c square where percentage error in a b

If P=[(A^2 B) /(C^3)] where percentage error in A, B and C...

If $\mathrm{P}=\left[\left(\mathrm{A}^{2} \mathrm{~B}\right) /\left(\mathrm{C}^{3}\right)\right]$ where percentage error in $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are respectively $\pm 2 \% \pm 3 \%$ and $\pm 5 \%$ then total percentage error in measurement of $\mathrm{p}$ (a) $18 \%$ (b) $14 \%$ (c) $21 \%$ (d) $12 \%$

If $\mathrm{P}=\left[\left(\mathrm{A}^{2} \mathrm{~B}\right) /\left(\mathrm{C}^{3}\right)\right]$ where percentage error in $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$
are respectively $\pm 2 \% \pm 3 \%$ and $\pm 5 \%$ then total percentage error in measurement of $\mathrm{p}$
(a) $18 \%$
(b) $14 \%$
(c) $21 \%$
(d) $12 \%$

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Key Concepts

Propagation of Errors

This concept deals with how uncertainties in measured quantities combine when those quantities are used in calculations. It involves determining the overall uncertainty in a result based on the individual uncertainties of the variables involved.

Percentage Error

Percentage error represents the error of a measurement expressed as a percentage relative to the true or accepted value. It is a normalized measure of error that helps compare uncertainties across different scales and magnitudes.

Error Propagation in Multiplication and Division

When quantities are multiplied or divided, the relative (or percentage) errors of the individual measurements add together to yield the overall relative error in the result. This linear addition of percentage errors is a key principle in the propagation of uncertainties in multiplicative relationships.

Effect of Exponents on Errors

When a measured quantity is raised to a power, the relative error in that measurement is multiplied by the exponent. This means if a variable with a certain percentage error is squared, the contribution of its uncertainty to the overall result is doubled.

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