Question

what is uncertainty is measurement explain the propagation of uncertainty in addition subtraction multiplication and division please answer in detail this is wrong question​

Answer 1

Answer:

Uncertainty: the possible range of error in the measurement is called uncertainty.

Explanation:o Types of uncertainty: there are two types of uncertainty.

1. Absolute uncertainty: the absolute uncertainty in a measurement is equal to least count of the measuring instrument.

Absolute uncertainty=Δx

2. Fractional uncertainty: the relative error in the measurement is called fractional uncertainty. It has no unit.

Mathematically: fractional uncertainty=error/measured value

%fractional uncertainty=Δx/x ×  100

Measurement of uncertainty=best estimate +- uncertainty

 Indicating uncertainty in calculation: in order to indicate uncertainty in the final result . the following rules are used:

1. Addition and subtraction rules: if two quantities A and B are added or subtracted then the absolute uncertainty in final result must be equal to the sum of absolute uncertainty in A and B.

i.e. Z=A±B  then ΔZ=ΔA+ΔB

Z=A-B  then ΔZ=ΔA+ΔB

 Product or division rule:  when two quantity A and B are multiplied or divide then  percentage frictional uncertainty in final result must be equal to the sum of percentage frictional uncertainty in A and B.

o Mathematically:  if  Z =A× B  Then,

%frictional uncertainty in Z =( %frictional uncertainty in A + %fractional uncertainty in B)

So, the product role will be=> Z ± ΔZ=AB ± (ΔA+ΔB)

  If  Z=A/B   Then,

%Frictional uncertainty in Z=%frictional uncertainty in A + %frictional uncertainty in B

So, the division rule will be=> Z ± ΔZ=A/B ± (ΔA+ΔB)

 Power role: when quantity appear in the form of power in an expression. Then percentage frictional uncertainty in final result must be equal to  power multiplied by percentage frictional uncertainty in that quantity at which power appear.

o Volume v=4/3 ᴫr2

o Area  A=4ᴫr2

o Time period t=2ᴫ √l/g