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Physics For Scientists & Engineers
Found in: Page 16

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Short Answer

A solid piece of lead has a mass of 23.94 gand a volume of 2.10 cm3.From these data, calculate the density of lead in SI units (kilograms per cubic meter).

The density of the solid piece of lead in SI unit is 11.4×103 kg/m3.

See the step by step solution

Step by Step Solution

Step 1:Definition and units of density of a substance

The amount of mass of any substance to its quantity or volume gives the density of that substance. Density is defined as the ratio of a mass to the volume of asubstance.

Density is measured inSI unit—kg/m3 andCGS unit—g/cm3

Unit conversion is a conversion of a unit of the same quantity from one unit to another using multiplication or division. It is a multistep process that involves multiplication/division by conversion factor

Step 2: Expression for the density of a substance and unit conversion

Write the expression for the density of the lead substance in terms of its mass and volume.

ρ=mV 1

Here, ρ is the density of the lead, m is mass of the lead, and V is volume of the lead.

Unit conversion method is used for the density measurements so that the final result will be close to the expected value.

Convert the unit 2.10 cm3 for volume V to m3 .

cm3=1×10-6 m32.10 cm3=2.10×10-6 m3

Convert the unit 23.94g for mass m to kg.

localid="1663589234857" 1g = 10-3 kg23.94 g = 23.94×10-3 kg

Step 3: Calculation of density of solid piece of lead in SI units

Replace 23.94×10-3kg for m and 2.10×10-6m3 for V in equation (1).

dρ=23.94×10-3 kg2.10×10-6 m3=11.4×103 kg/m3.

Hence, the density of the ρ of the solid piece of lead is 11.4×103 kg/m3.


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