Question 185: Units , Dimensions and Error Analysis

Question

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its
mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum
error in determining the density is:

Accepted Answer

Density of a material (d) = $${M \over {{L^3}}}$$
$$	herefore$$ Error in density,$${{\Delta d} \over d} = {{\Delta M} \over M} + 3{{\Delta L} \over L}$$
$${{\Delta d} \over d} 	imes 100 = {{\Delta M} \over M} 	imes 100 + 3{{\Delta L} \over L} 	imes 100$$
$$ \Rightarrow {{\Delta d} \over d} 	imes 100 = 1.5\%  + 3\left( 1 ight)\% $$ = 4.5 %

Answer

6%

Answer

2.5%

Answer

3.5%

Answer

4.5%

Units , Dimensions and Error Analysis

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:

Choose the correct answer: