QJEEM20Ph492c: JEE Main 2020 Physics - Class 11 JEEM20Ph492c Solution: A physical quantity z depends on four observables a, b, c and…

Question

Verified Solution • 2025–26 Session moderate

A physical quantity z depends on four observables
a, b, c and d, as z =

\frac{a^{2} b^{\frac{2}{3}}}{\sqrt{c} d^{3}}

. The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is :

Accepted Answer

z =

\frac{a^{2} b^{\frac{2}{3}}}{\sqrt{c} d^{3}}

\Rightarrow

\frac{d z}{z} \times 100 = (2 \frac{d a}{a} + \frac{2}{3} \frac{d b}{b} + \frac{1}{2} \frac{d c}{c} + 3 \frac{d (d)}{d}) \times 100

% error in z

=

(2 \times 2 + \frac{2}{3} \times 1.5 + \frac{1}{2} \times 4 + 3 \times 2.5)

%

= ( 4 + 1 + 2 + 7.5 ) %

= 14.5 %

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