Why should the measurement of physical quanti | vedclass

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

Question

(B) If a physical quantity is raised to a power $n$ (i.e.,$x^n$),the relative error in the result is given by $n 	imes (\Delta x / x)$.As the exponen

Vedclass · Accepted Answer

Because the relative error in a quantity with a large exponent is multiplied by the exponent,leading to a significant increase in the final relative error.

Vedclass · Answer

(B) If a physical quantity is raised to a power $n$ (i.e.,$x^n$),the relative error in the result is given by $n 	imes (\Delta x / x)$.As the exponent $n$ increases,the relative error in the measurement is magnified by a factor of $n$.Therefore,even a small error in the initial measurement of $x$ can lead to a large error in the final result.To ensure the final result remains within acceptable limits of accuracy,the initial measurement of quantities with large exponents must be performed with very high precision.

Why should the measurement of physical quantities with large exponents in an experiment be taken with high precision?

Similar Questions

$A$ physical quantity $P$ is given by $P = \frac{A^3 B^{1/2}}{C^{-4} D^{3/2}}$. The quantity which brings in the maximum percentage error in $P$ is

$A$ current of $(2.5 \pm 0.05) \ A$ flows through a wire and develops a potential difference of $(10 \pm 0.1) \ V$. The resistance of the wire in $\Omega$ is:

"It is advisable to use an instrument with the smallest possible least count." Explain this statement.

$A$ 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

In the density measurement of a cube,the mass and edge length are measured as $(10.00 \pm 0.10) \, kg$ and $(0.10 \pm 0.01) \, m$ respectively. The error in the measurement of density is

Vedclass Test Series

Exam Paper Generator

Online Exam Module