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  • A silver wire has a mass <img alt="\mathrm{\left ( 0.6\pm 0.006 \right )g}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cleft%20%28%200.6%5Cpm%200.006%20%5Cright%20%29g%

A silver wire has a mass \mathrm{\left ( 0.6\pm 0.006 \right )g} , radius \mathrm{\left ( 0.5\pm 0.005 \right )mm} and length \mathrm{\left ( 4\pm 0.04 \right )cm} . The maximum percentage error in the measurement of its density will be :

Option: 1

\mathrm{4\%}


Option: 2

\mathrm{3%}


Option: 3

\mathrm{6%}


Option: 4

\mathrm{7%}


Answers (1)

best_answer

\mathrm{density \left ( \rho \right )=\frac{\text { mass }}{\text { volume }}=\frac{m}{\pi r^{2} l} }

\mathrm{\frac{\Delta \rho }{p} \times 100} =\left(\frac{\Delta m}{m}+\frac{2 \Delta r}{r}+\frac{\Delta l}{l}\right) \times 100 \\

                    \mathrm{=\left(\frac{0.006}{0.6}+\frac{2 \times 0.005}{0.5}+\frac{0.04}{4}\right) \times 100} \\

                    \mathrm{=1+2+1 }\\

                    \mathrm{=4 \%}

Hence the correct answer is option 1.

Posted by

himanshu.meshram

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