The percentage errors in measurements of mass | vedclass

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

Question

(C) The kinetic energy $(KE)$ of a body is given by the formula: $KE = \frac{1}{2}mv^2$.Using the rules of error propagation for multiplication and po

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) The kinetic energy $(KE)$ of a body is given by the formula: $KE = \frac{1}{2}mv^2$.Using the rules of error propagation for multiplication and powers,the relative error in $KE$ is given by:$\frac{\Delta KE}{KE} = \frac{\Delta m}{m} + 2 \frac{\Delta v}{v}$.To find the percentage error,we multiply by $100$:$\frac{\Delta KE}{KE} 	imes 100 = \left( \frac{\Delta m}{m} 	imes 100 ight) + 2 \left( \frac{\Delta v}{v} 	imes 100 ight)$.Given that the percentage error in mass $\frac{\Delta m}{m} 	imes 100 = 2 \%$ and the percentage error in speed $\frac{\Delta v}{v} 	imes 100 = 3 \%$,we substitute these values:Percentage error in $KE = 2 \% + 2(3 \%) = 2 \% + 6 \% = 8 \%$.

The percentage errors in measurements of mass and speed of a body are $2 \%$ and $3 \%$ respectively. What is the percentage error in kinetic energy of the body (in $\%$)?

Similar Questions

Explain least count and least count error. Write a note on least count error.

The percentage error in the measurement of mass of a body and its speed are $0.73\%$ and $1.84\%$ respectively. The percentage error in the measurement of its momentum and kinetic energy are respectively

The length and breadth of a rectangle are $(5.7 \pm 0.1) \text{ cm}$ and $(3.4 \pm 0.2) \text{ cm}$,respectively. Calculate the area of the rectangle with error limits.

The acceleration due to gravity is measured on the surface of the Earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively,then the percentage error in the measurement of acceleration due to gravity is:

Write the types of errors in the measurement of a physical quantity and explain them.

Vedclass Test Series

Exam Paper Generator

Online Exam Module