Assertion : When percentage errors in the mea | vedclass

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

Question

(A) The kinetic energy $E$ is given by the formula $E = \frac{1}{2}mv^2$.Taking the relative error,we use the formula for propagation of errors:$\frac

Vedclass · Accepted Answer

If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

Vedclass · Answer

(A) The kinetic energy $E$ is given by the formula $E = \frac{1}{2}mv^2$.Taking the relative error,we use the formula for propagation of errors:$\frac{\Delta E}{E} = \frac{\Delta m}{m} + 2\frac{\Delta v}{v}$.Given that the percentage error in mass $\frac{\Delta m}{m} 	imes 100 = 1\%$ and the percentage error in velocity $\frac{\Delta v}{v} 	imes 100 = 2\%$.Substituting these values into the error equation:$\frac{\Delta E}{E} 	imes 100 = (\frac{\Delta m}{m} 	imes 100) + 2 	imes (\frac{\Delta v}{v} 	imes 100)$$\frac{\Delta E}{E} 	imes 100 = 1\% + 2 	imes 2\% = 1\% + 4\% = 5\%$.Since both the Assertion and the Reason are correct and the Reason correctly explains the propagation of error formula used in the Assertion,the correct option is $A$.

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

Similar Questions

If $x = a - b$,then the percentage error in $x$ will be

$A$ body travels uniformly a distance of $(13.8 \pm 0.2) \text{ m}$ in a time $(4.0 \pm 0.3) \text{ s}$. Its velocity with error limits and percentage error is

The percentage error in the measurement of $g$ is $.....\%$ (Given that $g = \frac{4 \pi^2 L}{T^2}$,$L = (10 \pm 0.1) \, cm$,$T = (100 \pm 1) \, s$)

The maximum error in the measurement of the density and mass of the uniform cube are $8\%$ and $2\%$ respectively. Hence, the maximum error in the measurement of length will be (in $\%$)

The resistance $R = \frac{V}{I}$,where $V = 100 \pm 5 \, \text{volts}$ and $I = 10 \pm 0.2 \, \text{amperes}$. What is the total percentage error in $R$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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