Question

a physical quantity p= a.b/c.d.The % error in measurement of a,b,c and d are 1%,3%,4% and 2%. what is the% error in measurement of p?​

Answer 1

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• Given :

=> Percentage error in a,b,c and d is respectively 1%,3%,4% and 2%

• To Find :

=> Percentage error in p

• Formula :

=> Percentage error in p is given by...

$\boxed {\sf{ \bold{ \pink{ \frac{\delta \: p}{p} = ( \frac{ \delta \: a}{a} + \frac{ \delta \: b}{b} + \frac{ \delta \: c}{c} + \frac{ \delta \: d}{d} ) \: }}}}$

• Calculation :

$\implies \sf \: { \bold{ \frac{ </strong><strong>\delta \: p}{p} = (1 </strong><strong>+ 3</strong><strong> + 4 </strong><strong>+ 2</strong><strong>) = 10</strong><strong>}} \\ \\ \: \: \: \: \: \: \: \: \: \boxed {\sf{ \boxed{ \bold{ \blue{per. \: error \: in \: p = 10</strong><strong> </strong><strong>}}}}}$

Answer 2

%dP/P = %dA/A + %dB/B + %dC/C + %dD/D

%dP/P = 1% + 3% + 4% + 2% = 10%