A physical quantity P is related to four obse | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the relation: $P = \frac{a^3 b^2}{c^{1/2} d}$.The relative error in $P$ is given by: $\frac{\Delta P}{P} = 3 \frac{\Delta a}{a} + 2 \frac{\D

Vedclass · Accepted Answer

$13 \%, 3.8$

Vedclass · Answer

(A) Given the relation: $P = \frac{a^3 b^2}{c^{1/2} d}$.The relative error in $P$ is given by: $\frac{\Delta P}{P} = 3 \frac{\Delta a}{a} + 2 \frac{\Delta b}{b} + \frac{1}{2} \frac{\Delta c}{c} + \frac{\Delta d}{d}$.To find the percentage error: $\left( \frac{\Delta P}{P} 	imes 100 ight) \% = \left( 3 	imes \frac{\Delta a}{a} 	imes 100 + 2 	imes \frac{\Delta b}{b} 	imes 100 + \frac{1}{2} 	imes \frac{\Delta c}{c} 	imes 100 + \frac{\Delta d}{d} 	imes 100 ight) \%$.Substituting the given percentage errors: $\left( \frac{\Delta P}{P} 	imes 100 ight) \% = (3 	imes 1 + 2 	imes 3 + 0.5 	imes 4 + 2) \% = (3 + 6 + 2 + 2) \% = 13 \%$.The calculated value of $P$ is $3.763$. Since the percentage error is $13 \%$,which has two significant figures,the result should be rounded off to two significant figures. Thus,$3.763$ rounded to two significant figures is $3.8$.

Similar Questions

$A$ physical quantity $S$ is related to four observables $a, b, c$, and $d$ as $S = \frac{\sqrt{a} b}{c^3 d^4}$. If the percentage errors of measurement in $a, b, c$, and $d$ are $2 \%$, $1 \%$, $1 \%$, and $1 \%$ respectively, then the percentage error in the quantity $S$ is: (in $\%$)

The maximum percentage errors in the measurement of mass $(M)$,radius $(R)$,and angular velocity $(\omega)$ of a ring are $2 \%$,$1 \%$,and $1 \%$ respectively. Find the maximum percentage error in the measurement of its angular momentum $(J = I \omega)$ about its geometrical axis. (in $\%$)

The percentage error in the measurement of a physical quantity $m$ given by $m = \pi \tan \theta$ is minimum when $\theta = \dots \dots \dots \dots \dots ^\circ$ (Assume that the error in $\theta$ remains constant).

Two resistances $60 \pm 0.36 \ \Omega$ and $30 \pm 0.09 \ \Omega$ are connected in parallel. The equivalent resistance is

Vedclass Test Series

Exam Paper Generator

Online Exam Module