If Q= frac{X^n}{Y^m} and Delta X is absolute error in the measurement of X, Delta Y is absolute

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1.Units, Dimensions and Measurement

easy

If $Q= \frac{X^n}{Y^m}$ and $\Delta X$ is absolute error in the measurement of $X,$ $\Delta Y$ is absolute error in the measurement of $Y,$ then absolute error $\Delta Q$ in $Q$ is

$\Delta Q = \pm \left( {n\frac{{\Delta X}}{X} + m\frac{{\Delta Y}}{Y}} \right)$

$\Delta Q = \pm \left( {n\frac{{\Delta X}}{X} + m\frac{{\Delta Y}}{Y}} \right)Q$

$\Delta Q = \pm \left( {n\frac{{\Delta X}}{X} - m\frac{{\Delta Y}}{Y}} \right)Q$

$\Delta Q = \pm \left( {n\frac{{\Delta X}}{X} - m\frac{{\Delta Y}}{Y}} \right)$

Solution

$\because \frac{\Delta \mathrm{Q}}{\mathrm{Q}}=\pm\left(\mathrm{n} \frac{\Delta \mathrm{x}}{\mathrm{x}}+\mathrm{m} \frac{\Delta \mathrm{y}}{\mathrm{y}}\right)$

$\Delta \mathrm{r} \Delta \mathrm{Q}=\pm\left(\mathrm{n} \frac{\Delta \mathrm{x}}{\mathrm{x}}+\mathrm{m} \frac{\Delta \mathrm{y}}{\mathrm{y}}\right) \mathrm{Q}$

Standard 11

Physics

The percentage errors in quantities $P, Q, R$ and $S$ are $0.5\%,\,1\%,\,3\%$ and $1 .5\%$ respectively in the measurement of a physical quantity $A\, = \,\frac{{{P^3}{Q^2}}}{{\sqrt {R}\,S }}$ . the maximum percentage error in the value of $A$ will be ……….. $\%$

hard

(JEE MAIN-2018)

The resistance $R =\frac{V}{I}$ where $V= 100 \pm 5 \,volts$ and $ I = 10 \pm 0.2$ amperes. What is the total error in $R$ ……… $\%$

medium

The resistance $R=V / I$ where $V=(100 \pm 5)\;V$ and $I=(10 \pm 0.2) \;A$. Find the percentage error in $R .$

easy

The length and width of a rectangular room are measured to be $3.95 \pm 0.05 \,m$ and $3.05 \pm 0.05 \,m$, respectively. The area of the floor is ……………….. $m^2$

medium

(KVPY-2016)

The current voltage relation of diode is given by $I=(e^{1000V/T} -1)\;mA$, where the applied voltage $V$ is in volts and the temperature $T$ is in degree Kelvin. If a student makes an error measuring $ \mp 0.01\;V$ while measuring the current of $5\; mA$ at $300\; K$, what will be the error in the value of current in $mA$ ?