(A) Given the formula $x = \frac{a^{1/2} b^2}{c^3}$.The relative error in $x$ is given by the expression:$\frac{\Delta x}{x} = \frac{1}{2} \frac{\Delt

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(A) Given the formula $x = \frac{a^{1/2} b^2}{c^3}$.The relative error in $x$ is given by the expression:$\frac{\Delta x}{x} = \frac{1}{2} \frac{\Delta a}{a} + 2 \frac{\Delta b}{b} + 3 \frac{\Delta c}{c}$.Substituting the given percentage errors:$\frac{\Delta x}{x} \times 100 = \frac{1}{2} (\pm 1\%) + 2 (\pm 3\%) + 3 (\pm 2\%)$.Calculating the maximum possible percentage error:$= \pm 0.5\% \pm 6\% \pm 6\% = \pm 12.5\%$.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

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An experiment measures quantities $a, b,$ and $c$ and then $x$ is calculated from $x = \frac{a^{1/2} b^2}{c^3}.$ If the percentage errors in $a, b,$ and $c$ are $\pm 1\%, \pm 3\%,$ and $\pm 2\%$ respectively,then the percentage error in $x$ is:

A
$\pm 12.5\%$
B
$\pm 7\%$
C
$\pm 1\%$
D
$\pm 4\%$

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Units, Dimensions and Measurement

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Dimensional Analysis, Uses and Limitations

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An experiment measures quantities $a, b,$ and $c$ and then $x$ is calculated from $x = \frac{a^{1/2} b^2}{c^3}.$ If the percentage errors in $a, b,$ and $c$ are $\pm 1\%, \pm 3\%,$ and $\pm 2\%$ respectively,then the percentage error in $x$ is:

Similar Questions

If the velocity of light $c$,universal gravitational constant $G$,and Planck's constant $h$ are chosen as fundamental quantities,the dimensions of mass in the new system are:

The dimensions of the area $A$ of a black hole can be written in terms of the universal gravitational constant $G$,its mass $M$ and the speed of light $c$ as $A=G^\alpha M^\beta c^\gamma$. Here,

Which of the following statements is incorrect?

The quantum Hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge,then the dimension of $R_H$ is the same as

If the speed of light $(c)$,acceleration due to gravity $(g)$,and pressure $(p)$ are taken as the fundamental quantities,then the dimension of the gravitational constant $(G)$ is:

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