If a, b, c are the percentage errors in the m | vedclass

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

Question

(B) Let $X = ABC$. Taking the natural logarithm on both sides,we get $\ln X = \ln A + \ln B + \ln C$. Differentiating both sides,we get $\frac{dX}{X}

Vedclass · Accepted Answer

$a + b + c$

Vedclass · Answer

(B) Let $X = ABC$. Taking the natural logarithm on both sides,we get $\ln X = \ln A + \ln B + \ln C$. Differentiating both sides,we get $\frac{dX}{X} = \frac{dA}{A} + \frac{dB}{B} + \frac{dC}{C}$. For small errors,this can be written as $\frac{\Delta X}{X} = \frac{\Delta A}{A} + \frac{\Delta B}{B} + \frac{\Delta C}{C}$. Given that $a, b, c$ are the percentage errors,we have $a = \frac{\Delta A}{A} 	imes 100$,$b = \frac{\Delta B}{B} 	imes 100$,and $c = \frac{\Delta C}{C} 	imes 100$. Therefore,the percentage error in $X = ABC$ is $\frac{\Delta X}{X} 	imes 100 = (\frac{\Delta A}{A} 	imes 100) + (\frac{\Delta B}{B} 	imes 100) + (\frac{\Delta C}{C} 	imes 100) = a + b + c$.

If $a, b, c$ are the percentage errors in the measurement of $A, B$ and $C$,then the percentage error in $ABC$ would be approximately

Similar Questions

$Assertion$ : When percentage errors in the measurement of mass and velocity are $1\%$ and $2\%$ respectively,the percentage error in $K.E.$ is $5\%$.
$Reason$ : $\frac{{\Delta E}}{E} = \frac{{\Delta m}}{m} + \frac{{2\Delta v}}{v}$

The resistance $R = \frac{V}{I}$,where $V = (50 \pm 2) \; V$ and $I = (20 \pm 0.2) \; A$. The percentage error in $R$ is $x\%$. The value of $x$ to the nearest integer is .........

The length of a pendulum is measured as $1.01 \ m$ and the time for $30$ oscillations is measured as $1 \ minute \ 3 \ s$. The error in length is $0.01 \ m$ and the error in time is $3 \ s$. The percentage error in the measurement of acceleration due to gravity is: (in $\%$)

The mean time period of a second's pendulum is $2.00 \, s$ and the mean absolute error in the time period is $0.05 \, s$. To express the maximum estimate of error,the time period should be written as:

The percentage errors in quantities $P, Q, R$ and $S$ are $0.5\%, 1\%, 3\%$ and $1.5\%$ respectively in the measurement of a physical quantity $A = \frac{P^3 Q^2}{\sqrt{R} S}$. The maximum percentage error in the value of $A$ will be ........... $\%$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module