Test: Measurement & Error Analysis - JEE MCQ

According to the problem time for 20 oscillations of a pendulum 

t₁ ​= 3 9.6s,  t₂ ​= 39.9s,  t₃​ =3 9.5s

It is quite obvious from these observations that the least count by the water is 0.1s. As measurements have only one decimal place.

► Precision in measurement = least count of measuring instrument = 0.1s

► Precision in 20 oscillations = 0.1

Therefore, Precision in 1 oscillation = 0.1/ 20​= 0.005.

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 = (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.