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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.

Ωxρ(x,y,z)dV

Short Answer

Expert verified

Quantity: First momentum

The unit for momentum is grams centimeter.

Step by step solution

01

Step 1. Given information.

Given:

Ωxρ(x,y,z)dV

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

02

Step 2. Identify the quantity

The objective of the problem is to describe about the triple integral Ωxρ(x,y,z)dvand find its units.

By the definition of the first momentum M of the solidΩ the triple integral first

momentum.

Hence the given relation represents the first momentum M of the solid Ω

Since if ρrepresents the density of the solid Ωthen Ωxρ(x,y,z)dvrepresents the first momentum.

The unit for momentum is grams centimeter.

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