Examkin

Soru

Zorluk: OrtaErrors in Measurement and Significant Figures

In a laboratory experiment, the radius of a circular wire is measured as (2.00±0.05) mm(2.00 \pm 0.05)\text{ mm}. What is the percentage error in the calculated cross-sectional area of the wire?

  1. A
    2.5%2.5\%
  2. 5.0%5.0\%Cevap
  3. C
    6.25%6.25\%
  4. D
    1.25%1.25\%

Cevap

The percentage error in the calculated area is 5.0%5.0\%.
The cross-sectional area of a wire is given by A=πr2A = \pi r^2. The percentage error in a calculated quantity y=xny = x^n is given by n×(percentage error in x)n \times (\text{percentage error in } x). Here, the percentage error in the radius rr is (0.05/2.00)×100%=2.5%(0.05 / 2.00) \times 100\% = 2.5\%. Multiplying by the power n=2n = 2 gives 2×2.5%=5.0%2 \times 2.5\% = 5.0\%.

Adım Adım Çözüm

1
Calculate the percentage error in the measured radius rr.
Percentage error in r=(0.052.00)×100%=2.5%\text{Percentage error in } r = \left(\frac{0.05}{2.00}\right) \times 100\% = 2.5\%
Relative error is the absolute error divided by the measured value.
2
Apply the rule of error propagation for quantities raised to a power (A=πr2A = \pi r^2).
Percentage error in A=2×(Percentage error in r)=2×2.5%=5.0%\text{Percentage error in } A = 2 \times (\text{Percentage error in } r) = 2 \times 2.5\% = 5.0\%
When a physical quantity is raised to the power nn, its fractional or percentage error is multiplied by nn.

Anahtar Kavram

Error Propagation in Derived Quantities
Tahmini Süre:1m 30s
Bu soruyu puanla

Konular

Errors in Measurement and Significant Figures

Bu konudan daha fazla soru