A physical quantity z depends on fout observables a , b , c and d, as z =( a 2 b (2/3)/√ c d 3) The percentage of error in the measurement of a, b, c and d 2 %, 1.5 %, 4 % and 2.5 % respectively. The percentage of error in z is:

Question

A physical quantity z depends on fout observables a , b , c and d, as z =( a 2 b (2/3)/√ c d 3) The percentage of error in the measurement of a, b, c and d 2 %, 1.5 %, 4 % and 2.5 % respectively. The percentage of error in z is: (A) 12.25 % (B) 14.5 % (C) 16.5 % (D) 13.5 %

Tardigrade Admin · Accepted Answer

Given: z=(a2 b2 / 3/√c d3) Percentage error in Z, (Δ Z/Z)=(2 Δ a/a)+(2 Δ b/3 b)+(1 Δ c/2 c)+(3 Δ d/d) =2 × 2+(2/3) × 1.5+(1/2) × 4+3 × 2.5=14.5 %

Q. A physical quantity $z$ depends on fout observables $a, b, c$ and $d$ , as $z = \frac{a ^{2} b ^{\frac{2}{3}}}{c d ^{3}}$ The percentage of error in the measurement of $a, b, c$ and $d$ $2%, 1.5%, 4%$ and $2.5%$ respectively. The percentage of error in $z$ is:

$12.25%$

$14.5%$

$16.5%$

$13.5%$

Given: $z = \frac{a ^{2} b ^{2/3}}{c d ^{3}}$
Percentage error in Z,
$\frac{Δ Z}{Z} = \frac{2Δ a}{a} + \frac{2Δ b}{3 b} + \frac{1Δ c}{2 c} + \frac{3Δ d}{d}$
$= 2 \times 2 + \frac{2}{3} \times 1.5 + \frac{1}{2} \times 4 + 3 \times 2.5 = 14.5%$

Q. A physical quantity z depends on fout observables a,b,c and d, as z=c​d3a2b32​​ The percentage of error in the measurement of a,b,c and d 2%,1.5%,4% and 2.5% respectively. The percentage of error in z is:

12.25%

14.5%

16.5%

13.5%