Question

what do you mean by propagation of errors? explain the propagation of errors in addition and multiplication. ​

Answer 1

Answer:

When you want calculate the area of a square plate, for that you need to measure the length of one side of the plate. Now if you a have scale with only centimeter markings and you'll be able to measure only to the nearest centimeter. there'll be errors in you measurement.

Now if you take that length with error and calculate the area, the area will also have error. This is called propagation of error, it has propagated from length to area.

Like this whenever there are errors in measurements, the errors propagate to the physical quantities we calculate using the variables with errors.

In real world we cant get rid of errors but we'll be able to know how much it impacts the calculations.

ex: lets say a 'P' is some physical quantity dependent on 'J','L' and 'K' as

P = JᵃKᵇL⁻ⁿ

error in 'P' (denoted by 'ΔP') is given by

ΔP/P = ±(aΔJ/J + bΔK/K + nΔL/L)

(even when the powers are negative you have to add the errors)

Answer 2

$\textbf{Answer is in attachment!}$