A physical quantity A is related to four observable a,b,c and d as follows, A = frac{{{a^2}{b^3}}}{{csqrt d }}, the percentage errors of measurement in

Q: A physical quantity $A$ is related to four observable $a,b,c$ and $d$ as follows, $A = \frac{{{a^2}{b^3}}}{{c\sqrt d }}$, the percentage errors of measurement in $a,b,c$ and $d$ are $1\%,3\%,2\% $ and $2\% $ respectively. What is the percentage error in the quantity $A$ ......... $\%$

d $A =\frac{ a ^{2} b ^{3}}{ c \sqrt{ d }}$ $\frac{\Delta a }{ a } \times 100=1 \%,$$ \frac{\Delta b }{ b } \times 100=3 \%,$$ \frac{\Delta c }{ c } \times 100=2 \%$ and $\frac{\Delta d }{ d } \times 100=2 \%$ $\frac{\Delta A }{ A } \times 100=2 \frac{\Delta a }{ a } \times 100+3 \frac{\Delta b }{ b } \times 100+$$\frac{\Delta c }{ c } \times 100+\frac{1}{2} \times \frac{\Delta d }{ d } \times 100$ $\frac{\Delta A }{ A } \times 100=2 \times 1+3 \times 3+2+\frac{1}{2} \times 2=14 \%$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

A physical quantity $A$ is related to four observable $a,b,c$ and $d$ as follows, $A = \frac{{{a^2}{b^3}}}{{c\sqrt d }}$, the percentage errors of measurement in $a,b,c$ and $d$ are $1\%,3\%,2\% $ and $2\% $ respectively. What is the percentage error in the quantity $A$ ......... $\%$

A$12$
B$7$
C$5$
D$14$

Medium

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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