If there is a positive error of 50% in the me | vedclass

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

Question

(D) The kinetic energy $E$ of a body is given by $E = \frac{1}{2}mv^2$.Since $m$ is constant,the relative change in kinetic energy is related to the v

Vedclass · Accepted Answer

$125$

Vedclass · Answer

(D) The kinetic energy $E$ of a body is given by $E = \frac{1}{2}mv^2$.Since $m$ is constant,the relative change in kinetic energy is related to the velocity $v$ by the relation $\frac{\Delta E}{E} \approx 2 \frac{\Delta v}{v}$.Given the percentage error in velocity is $\frac{\Delta v}{v} 	imes 100 = 50\%$,which means the new velocity $v' = v + 0.5v = 1.5v$.The new kinetic energy $E'$ is $E' = \frac{1}{2}m(v')^2 = \frac{1}{2}m(1.5v)^2 = 2.25 	imes (\frac{1}{2}mv^2) = 2.25E$.The percentage error in kinetic energy is $\frac{E' - E}{E} 	imes 100 = \frac{2.25E - E}{E} 	imes 100 = 1.25 	imes 100 = 125\%$.

If there is a positive error of $50\%$ in the measurement of velocity of a body,then the error in the measurement of kinetic energy is .............. $\%$

Similar Questions

Which of the following comes under the category of random errors?

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 $R$?

$A$ force $F$ is applied on a square area of side $L$. If the percentage error in the measurement of $L$ is $2 \%$ and that in $F$ is $4 \%$,what is the maximum percentage error in pressure (in $\%$)?

If two resistors have resistances $R_1 = (350 \pm 3) \text{ } \Omega$ and $R_2 = (140 \pm 4) \text{ } \Omega$, then the percentage error for the sum and difference of $R_1$ and $R_2$ are respectively:

The mass of an empty beaker is $(10.1 \pm 0.1) \, g$. When it is completely filled with a liquid,its mass becomes $(17.3 \pm 0.1) \, g$. What is the best value for the mass of the liquid within the possible limits of accuracy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module