Test: Measurement And Error Analysis

Given,
t₁ = 39.6 s
t₂ = 39.9s
t₃ = 39.5 s
Least count of measuring instrument = 0.1 s
[As measurements have only one decimal place] Percision in the measurement  = Least count of the measuring instrument =0.1 s
Mean value of time for 20 oscillations

Absolute errors in the measurements
Δt₁ = t - t₁ = 39.7 - 39.6 = 0.1s
Δt₂ = t - t_{2 = 39.7 - 39.9 = -0.2 s}
Δt₃ = t - t_{3 = 39.7 - 39.5 = 0.2 s}

_{Mean absolute error}

∴ Accuracy of measurement =±0.2s.

Gross errors are mostly due to lack of knowledge, judgment and care on the part of experiment. That is Gross error is caused by careless handling.

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=4πr³/3

 % error is volume=3×error in radius   =3×1= 3%

absolute error = 0.01-0.03 /2 = -0.01

Mean absolute error = (|0.01 -(-0.01)|+|-0.03-(-0.01)|)/2
= (0.02+0.02)/2

= 0.02

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.

Multiply the exponents with their respective bases and add them. Remember that, error can only be added and not subtracted.

= 2 x a + 3 x b + 1 x d + 1/2 x c

= 2 x 1% + 3 x 3% + 1 x 1% + 1/2 x 2%

= 2% + 9% + 1% + 1%

= 13%