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

$A$ system has basic dimensions as density $[D]$,velocity $[V]$,and area $[A]$. The dimensional representation of force in this system is:

Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities,namely,the gravitational constant $G$,Planck's constant $h$,and the speed of light $c$,as $Y = c^\alpha h^\beta G^\gamma$. Which of the following is the correct option?

Using dimensional analysis,the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as

Check that the ratio $ke^{2} / G m_{e} m_{p}$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

In a new system of units,energy $(E)$,density $(d)$,and power $(P)$ are taken as fundamental units. Then the dimensional formula of the universal gravitational constant $G$ will be .......

Vedclass Test Series

Exam Paper Generator

Online Exam Module