Question 229: Units , Dimensions and Error Analysis

Question

The density of a solid metal sphere is determined by measuring its mass and its diameter. The
maximum error in the density of the sphere is $$\left( {{x \over {100}}} \right)$$ %.  If the relative errors in measuring the mass
and the diameter are 6.0% and 1.5% respectively, the value of x is_______.

Accepted Answer

$$ho $$ = $${M \over V}$$ = $${M \over {{4 \over 3}\pi {{\left( {{D \over 2}} ight)}^3}}}$$
$$ \Rightarrow $$ $$ho $$ = $${6 \over \pi }M{D^{ - 3}}$$
For maximum error
$${{dho } \over ho } 	imes 100 = {{dM} \over M} 	imes 100 + 3{{dD} \over D} 	imes 100$$
= 6 + 3 $$ 	imes $$ 1.5
= 10.5 %
= $$\left( {{{1050} \over {100}}} ight)$$ %
$$ 	herefore $$ x = 1050

Units , Dimensions and Error Analysis

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $\left( {{x \over {100}}} \right)$ %. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is_______.

Integer / Numeric Answer Type