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Identify the quantities determined by the integral expressions in Exercises 19–24. If x, y, and z are all measured in centimeters and ρ(x, y,z) is a density function in grams per cubic centimeter on the three-dimensional region , give the units of the expression.

Ωzρ(x,y,z)dV

Short Answer

Expert verified

Quantity: Centre of mass

No unit.

Step by step solution

01

Step 1. Given information.

Given:

Ωzρ(x,y,z)dV

We have to identify the quantities determined by the given integral expression.

02

Step 2. Identify the quantity

By definition 13.19, z¯=Mxymrepresents the third ordinate z of centre of mass of role="math" localid="1650350428786" Ω

Hence the given relation represents the third ordinate z of centre of mass of

Ω

Thus, There are no units for centre of mass.

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