Length, breadth and thickness of a strip are (10.0 pm 0.1) cm ,(1.00 pm 0.01) cm and (0.100 pm 0.001

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1.Units, Dimensions and Measurement

easy

The length, breadth and thickness of a strip are $(10.0 \pm 0.1)\; cm ,(1.00 \pm 0.01) \;cm$ and $(0.100 \pm 0.001)\; cm$ respectively. The most probable error in its volume will be?

$\pm \,0.03\, cm^{3}$

$\pm\, 0.111 \,cm^{3}$

$\pm\, 0.012\, cm^{3}$

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Solution

$V =L\times b\times w$

$ \frac{{\Delta V}}{V}\,\, \times \,\,100\,\, = \,\,\frac{{\Delta \ell }}{\ell }\,\, \times \,\,100\,\, + \,\frac{{\Delta w}}{w}\,\, \times \,\,100\,\, + \;\,\frac{{\Delta t}}{t}\,\, \times \,\,100$

$ = \,\,\frac{{0.1}}{{10}}\,\, \times \,\,100\,\, + \;\,\frac{{0.01}}{1}\,\, \times \,\,100\,\, + \;\,\frac{{0.001}}{{0.1}}\,\, \times \,\,100$

$= \,\,\left( {0.01\,\, + \;\,0.01\,\, + \;\,0.01} \right)\% \,\, = \,\,0.03\% \;\,$

Standard 11

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(JEE MAIN-2017)

The length, breadth and thickness of a strip are $(10.0 \pm 0.1)\; cm ,(1.00 \pm 0.01) \;cm$ and $(0.100 \pm 0.001)\; cm$ respectively. The most probable error in its volume will be?

Solution

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A physical quantity $p$ is described by the relation $p\, = a^{1/2}\, b^2\, c^3\, d^{-4}$

If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\% , 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be ……….. $\%$