Question

In an experiment to determine the density of a cube the percentage error in the measurement of mass is 0.26% and percentage error in the measurement of length is 0.38%. What will be the percentage error in the determine of its density?

Answer 1

density=mass/volume=mass/length^3

therefore percentage error=percentage error in mass+3 percentage error in length=0.26+3×0.38=1.4%

Answer 2

Answer:

The percentage error in the density is 1.4%

Explanation:

Given:

Percentage error in mass = 0.26%

Percentage error in length = 0.38%

To find:

The percentage error in density.

Formula:

$Density=\frac{Mass}{Volume}$

Step 1:

We know that volume of a cube is given by the cube of its side. Therefore,  $D=\frac{M}{L^{3} }$, where M is the mass of the cube and L is the length of its side.

In the case of fractions, the relative errors get added up and in the case of exponentials, it is multiplied by the power. So,

$\frac{dD}{D}=\frac{dM}{M}+3\frac{dL}{L}$

Step 2:

Substituting the given values, we get

$\frac{dD}{D}=0.0026+3(0.0038)$

$\frac{dD}{D}=0.0026+0.0114$

$\frac{dD}{D}=0.014$

$\frac{dD}{D}=$ 1.4%

Therefore, in the determination of the density of the given cube, the percentage error will be 1.4%

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