A physical parameter a can be determined by m | vedclass

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

Question

(D) Given the relation: $a = \frac{b^\alpha c^\beta}{d^\gamma e^\delta}$.According to the theory of propagation of errors,for a quantity $a = b^\alpha

Vedclass · Accepted Answer

$(\alpha {b_1} + \beta {c_1} + \gamma {d_1} + \delta {e_1})\%$

Vedclass · Answer

(D) Given the relation: $a = \frac{b^\alpha c^\beta}{d^\gamma e^\delta}$.According to the theory of propagation of errors,for a quantity $a = b^\alpha c^\beta d^{-\gamma} e^{-\delta}$,the maximum relative error is given by the sum of the relative errors of the individual components multiplied by their respective powers.The maximum percentage error is calculated as:$\left( \frac{\Delta a}{a} 	imes 100 ight)_{\max} = |\alpha| \left( \frac{\Delta b}{b} 	imes 100 ight) + |\beta| \left( \frac{\Delta c}{c} 	imes 100 ight) + |-\gamma| \left( \frac{\Delta d}{d} 	imes 100 ight) + |-\delta| \left( \frac{\Delta e}{e} 	imes 100 ight)$.Substituting the given percentage errors $b_1\%, c_1\%, d_1\%, e_1\%$:$\left( \frac{\Delta a}{a} 	imes 100 ight)_{\max} = (\alpha b_1 + \beta c_1 + \gamma d_1 + \delta e_1)\%$.Thus,the correct option is $D$.

Similar Questions

Find the relative error in $Z$,if $Z = \frac{A^{4} B^{1/3}}{C D^{3/2}}$.

The resistance $R = V / I$ where $V = (100 \pm 5) \; V$ and $I = (10 \pm 0.2) \; A$. Find the percentage error in $R$. (in $\%$)

The errors in the measurement of mass and length of a cube are $1.5 \%$ and $2.5 \%$ respectively. The percentage error in the measurement of the density of the cube is: (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module