In the measurement of a physical quantity X = | vedclass

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

Question

(C) Given the formula $X = \frac{A^2 B}{C^{1/3} D^3}$.Using the principle of propagation of errors, the relative error in $X$ is given by:$\frac{\Delt

Vedclass · Accepted Answer

$C$

Vedclass · Answer

(C) Given the formula $X = \frac{A^2 B}{C^{1/3} D^3}$.Using the principle of propagation of errors, the relative error in $X$ is given by:$\frac{\Delta X}{X} = 2 \left( \frac{\Delta A}{A} ight) + \left( \frac{\Delta B}{B} ight) + \frac{1}{3} \left( \frac{\Delta C}{C} ight) + 3 \left( \frac{\Delta D}{D} ight)$.Now, calculate the contribution of each term to the percentage error:Contribution from $A = 2 	imes 2 \% = 4 \%$.Contribution from $B = 1 	imes 2 \% = 2 \%$.Contribution from $C = \frac{1}{3} 	imes 4 \% = 1.33 \%$.Contribution from $D = 3 	imes 5 \% = 15 \%$.Comparing these values, the minimum contribution to the percentage error in $X$ is from $C$.

Similar Questions

If the error in the measurement of the radius of a sphere is $2\%$,then the error in the determination of the volume of the sphere will be ........ $\%$

The measurements of two quantities along with the precision of their respective measuring instruments are $A = 2.5 \, m/s \pm 0.5 \, m/s$ and $B = 0.10 \, s \pm 0.01 \, s$. The value of $AB$ will be:

$A$ particle covers a distance of $(13.8 \pm 0.2) \ m$ in $(4 \pm 0.3) \ s$. Its velocity under error limits will be

Zero error in an instrument introduces

The length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$,the percentage error in calculated volume of cylinder is ............. $\%$

Vedclass Test Series

Exam Paper Generator

Online Exam Module