The percentage error in the measurement of ma | vedclass

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

Question

(C) The kinetic energy $K$ of a body is given by the formula $K = \frac{1}{2}mv^2$,where $m$ is the mass and $v$ is the speed.Using the rules of propa

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(C) The kinetic energy $K$ of a body is given by the formula $K = \frac{1}{2}mv^2$,where $m$ is the mass and $v$ is the speed.Using the rules of propagation of errors,the relative error in kinetic energy is given by $\frac{\Delta K}{K} = \frac{\Delta m}{m} + 2 \frac{\Delta v}{v}$.Given that the percentage error in mass $\frac{\Delta m}{m} 	imes 100 = 3 \%$ and the percentage error in speed $\frac{\Delta v}{v} 	imes 100 = 4 \%$.Substituting these values into the error formula:Percentage error in $K = (3 \%) + 2 	imes (4 \%) = 3 \% + 8 \% = 11 \%$.Therefore,the percentage error in the measurement of kinetic energy is $11 \%$.

The percentage error in the measurement of mass and speed of a particular body is $3 \%$ and $4 \%$ respectively. The percentage error in the measurement of kinetic energy is (in $\%$)

Similar Questions

Error in the measurement of radius of a sphere is $0.2\%$. The error in the calculated value of its volume is ......... $\%$

In a simple pendulum experiment,the maximum percentage error in the measurement of length is $2\%$ and that in acceleration due to gravity $g$ is $4\%$. Then the maximum percentage error in determination of the time-period is

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3\%$ each,then the error in the value of resistance of the wire is ........ $\%$

If $P = \frac{A^3}{B^{5/2}}$ and $\Delta A$ is the absolute error in $A$ and $\Delta B$ is the absolute error in $B$,then the absolute error $\Delta P$ in $P$ is:

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