In an experiment,four quantities a, b, c and | vedclass

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

Question

(C) The formula for the relative error in $w$ is given by the propagation of errors rule:$\frac{\Delta w}{w} = 4 \frac{\Delta a}{a} + 3 \frac{\Delta b

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(C) The formula for the relative error in $w$ is given by the propagation of errors rule:$\frac{\Delta w}{w} = 4 \frac{\Delta a}{a} + 3 \frac{\Delta b}{b} + 2 \frac{\Delta c}{c} + \frac{1}{2} \frac{\Delta d}{d}$Given percentage errors are:$\frac{\Delta a}{a} 	imes 100 = 1\%$$\frac{\Delta b}{b} 	imes 100 = 2\%$$\frac{\Delta c}{c} 	imes 100 = 3\%$$\frac{\Delta d}{d} 	imes 100 = 4\%$Substituting these values into the error equation:$\frac{\Delta w}{w} 	imes 100 = 4(1\%) + 3(2\%) + 2(3\%) + \frac{1}{2}(4\%)$$= 4\% + 6\% + 6\% + 2\%$$= 18\%$Therefore,the percentage error in $w$ is $18\%$.

In an experiment,four quantities $a, b, c$ and $d$ are measured with percentage errors of $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $w$ is calculated as follows: $w = \frac{a^4 b^3}{c^2 \sqrt{d}}$. The percentage error in the measurement of $w$ is .......... $\%$.

Similar Questions

If the present units of length,time,and mass $(m, s, kg)$ are changed to $100 \; m, 100 \; s, 0.1 \; kg$,then:

The conversion of $1 \;MW$ power in a new system having basic units of mass,length,and time as $10 \;kg$,$1 \;dm$,and $1 \;minute$ respectively is:

If $C$ is the velocity of light,$h$ is Planck's constant,and $G$ is the gravitational constant,and these are taken as fundamental quantities,then the dimensional formula of mass is:

In the expression $A=B+\frac{C}{D+E}$,the dimensions of physical quantities $B$ and $C$ are $[L^{1} M^{0} T^{-1}]$ and $[L^{1} M^{0} T^{0}]$ respectively. The dimensions of quantities $A, D$ and $E$ are

From the following,the quantity (constructed from the basic constants of nature) that has the dimensions of length,as well as the correct order of magnitude for a typical atomic size,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module