Indirect Measurement

Figure 2: Caliper

Choose a spherical object and measure its radius multiple times with a caliper. Write the results in the following tables:

Questions :

1- Calculate the mean measured value. ρ ̅ =14.16

2- Calculate the error mean absolute ∆ρ ̅ =0.11

3- Calculate the mean squared uncertainty σ=0.13

4- Calculate the absolute uncertainty and relative v ̅ = 1.97..................∆v=0.03

5- gives the expressions of absolute uncertainty ∆ρ ̅ as a function of v, m, ∆v and ∆m

ρ = m v Δ ρ = | δ ρ δ m | Δ m + | δ ρ δ v | Δ v %rho = {m} over {v} rightarrow %DELTA %rho = lline { %delta %rho } over { %delta m} rline * %DELTA m+ lline { %delta %rho } over { %delta v} rline * %DELTA v
Δ ρ = Δ m v + Δ v m %DELTA %rho = { %DELTA m} over {v} + { %DELTA v} over {m}

6- Calculate the absolute uncertainty and relative ∆ρ= 0.04..........∆ρ/ρ ̅= 0.002

7 - Write the measured value in the fom : ρ = ρ ̅±∆ρ; ρ = 14.16±0.04