Question

maximum error in the measurement of a mass and length of a cube is 3% and 2% respectively. what will be the maximum error in the measurement of density

Answer 1

max error in mass = %m = 3%
max error in length = %l = 2%
max error in volume = %v = ?

V = l³

During the division and multification the resultant relative is the sum of relative error of individual quantities

∆V/V = 3(∆l/l)

multiply with 100 it becomes % error

∆V/V × 100 = 3(∆l/l × 100)

%V = 3(%l)

%V = 3(2%)

%V = 6%

density = mass/volume

∆p/p = ∆m/m + ∆v/v

∆p/p × 100 = (∆m/m × 100) + (∆v/v × 100)

%p = %m + %v

%p = 3% + 6%

%p = 9%

hence the max % error in measuring in the density is 9%

hence we can say that during the division and multification the resultant percentage (%) error is the sum of the percentage error of individual quantities.

[ note :-
during the addition and subtraction the resultant absolute error is the sum of error in individual quantities i.e ∆Z = ∆A + ∆B ]

Answer 2

Answer:

9 %

ok thankyou