Explain uncertainty or error in given measurement by suitable example.
Explain uncertainty or error in given measurement by suitable example.
$(1)$ Length and breadth of a thin rectangular plate is $l=16.2 \mathrm{~cm}$ and breadth $b=10.1 \mathrm{~cm}$ Least count of meterscale is $0.1 \mathrm{~cm}$ hence absolute error in measurement should be $0.1 \mathrm{~cm}$.
$l=(16.2 \pm 0.1) \mathrm{cm}$
$b=(10.1 \pm 0.1) \mathrm{cm}$
$\%$ error in measurement of length,
$l=(16.2 \pm 0.6 \%) \mathrm{cm}$
$\%$ error in measurement of breadth,
$b=(10.1 \pm 1 \%) \mathrm{cm}$
Area of rectangular plate,
$\mathrm{A} =l b$
$=16.2 \times 10.1=163.62 \mathrm{~cm}^{2}$
$\%$ error in $\mathrm{A}$ :
$=\frac{\Delta \mathrm{A}}{\mathrm{A}} \times 100=\frac{\Delta l}{l} \times 100+\frac{\Delta b}{b} \times 100$
$=(0.6 \%+1 \%)=1.6 \%$
$\Delta \mathrm{A} =\frac{1.6 \times 163.62}{100}=2.6$
Area : $\mathrm{A}=(163.62 \pm 2.6) \mathrm{cm}^{2}$
Here, minimum significant digit are $3$ hence area should be represented as, $\mathrm{A} \approx 163 \pm 3 \mathrm{~cm}^{2}$
$\therefore$ Error in measurement of area of plate is $3 \mathrm{~cm}^{2}$.
$(2)$ If a set of experimental data is specified to ' $n$ ' significant figures, a result obtained by combining the data will also be valid to ' $n$ ' significant figures.
However, if data is subtracted the number of significant figures can be reduced. For example,
$12.9 \mathrm{~g}-7.06 \mathrm{~g}=5.84 \mathrm{~g}$
Here, there are $3$ significant digits. But in subtraction digit after decimal point are considered hence this will be represented as $5.8 \mathrm{~g}$.
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