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1.Units, Dimensions and Measurement
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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 ........... $\%$
A
$8.5$
B
$6.0$
C
$7.5$
D
$6.5$
(JEE MAIN-2018)
Solution
$\begin{array}{l}
Maximum\,percentage\,error\,in\,A\\
= 3\left( {\% \,error\,in\,p} \right) + 2\left( {\% \,error\,in\,Q} \right)\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + \frac{1}{2}\left( {\% \,error\,in\,R} \right) + 1\left( {\% \,error\,in\,S} \right)\\
= 3 \times 0.5 + 2 \times 1 = \frac{1}{2} \times 3 + 1 \times 1.5\\
= 1.5 + 2 + 1.5 + 1.5 = 6.5\%
\end{array}$
Standard 11
Physics
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