Measurement & Error Analysis - Free MCQ Practice Test with solutions, NEET

Given:

t₁ = 39.6 s
t₂ = 39.9 s
t₃ = 39.5 s

Calculate the mean time

t̄ = (t₁ + t₂ + t₃) / 3

t̄ = (39.6 + 39.9 + 39.5) / 3

t̄ = 119.0 / 3 = 39.67 s

Calculate the mean absolute error

Δt = (|t₁ − t̄| + |t₂ − t̄| + |t₃ − t̄|) / 3

Δt = (|39.6 − 39.67| + |39.9 − 39.67| + |39.5 − 39.67|) / 3

Δt = (0.07 + 0.23 + 0.17) / 3

Δt = 0.47 / 3 = 0.16 s

Final Result:

t = (39.67 ± 0.16) s

Gross errors are primarily due to negligence, oversight, or lack of proper care during experimental procedures. Careless handling can lead to significant mistakes, such as incorrect measurements or misinterpretation of data, which are characteristic of gross errors. These types of errors are distinct from systematic or random errors, as they often result from human factors rather than inherent flaws in the experimental setup or measurement process.

From the releation

h= 1/2gt²  ⇒ g = 2h/t²

Taking natural logarithms on both sides, we get

ln (g)  = ln (h) - 2ln (t) + ln (2)

Differentiating

for maximum permissible errors , we add both the errors . so

∵ V = (4/3)πr³
% error is volume = 3 × error in radius = 3 × 1 = 3%

Absolute error 
Mean absolute error

Only electron microscope has resolution of 0.5-0.6 Angstrom which is less than the size of an atom.

Cesium 133 is the element most commonly chosen for atomic clocks.

The astronomers mainly use parallax method to find distances to objects like other planets. To calculate the distance to a star or to a planet, astronomers observe it from different places along Earth's orbit around the Sun.