(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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DifficultAIIMS 2008

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Frequency $(n)$ is a function of density $(\rho)$,length $(a)$,and surface tension $(T)$. Then its value is:

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EasyAP EAMCET 2024

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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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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

The speed of light $(c)$,gravitational constant $(G)$,and Planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be

$A$ force $F$ acting on an object is given by $F = a \sqrt{x} - bt$,where $x$ is the distance in meters and $t$ is the time in seconds. The units of $a$ and $b$ are respectively:

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