Question

In the density measurement of a cube, the mass and edge length are
measured as (15.00+ 0.20)kg and (0.30 = 0.01)m, respectively. The
relative error in the measurement of density is:​

Answer 1

Concept:

The error can be defined as the difference in two measurements of the same object of the same quantity.

Let, the formula of s = r²a³

The relative error in s can be calculated as,

Δs/s =  (2 Δr/r + 3 Δa/a)

Given:

The mass of cube, m =  (15.00 ± 0.20) kg

Edge length of the cube, s = (0.30 ± 0.01)m

Find:

The relative error in the measurement of the density, Δρ/ρ

Solution:

Density is defined as the product of mass and volume, here the object is a cube.

ρ = mV = ms³

The relative error is density, ρ,

Δρ/ρ =  ( Δm/m + 3 Δs/s)

Substituting the values,

Δρ/ρ =  ([0.20/15.00) + (3× 0.01/0.30)]

Δρ/ρ =  [(1/75) + (1/10)] = 17/150

Hence, the relative error in the measurement of density is 17/150.

#SPJ3