Chapter 14 Find the mass of the lamina described by the inequalities

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subject Authors Bruce H. Edwards, Ron Larson

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850 Chapter 14: Multiple Integration
14.4 Center of Mass and Moments of Inertia
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the mass of the lamina described by the inequalities
given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.)
a. 768
b. 128
c. 512
d. 256
e. 392
____ 2. Find the mass of the lamina described by the inequalities
given that its density is . (Hint: Some of the integrals
are simpler in polar coordinates.)
a.
b.
c.
d.
e.
____ 3. Find the center of mass of the rectangular lamina with vertices
and for the density .
a.
b.
c.
d.
e.
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14.4 Center of Mass and Moments of Inertia 851
____ 4. Find the center of mass of the rectangular lamina with vertices
for the density .
a.
b.
c.
d.
e.
____ 5. Find the mass of the triangular lamina with vertices for
the density .
a. 401k
b. 809k
c. 800k
d. 400k
e. 805k
____ 6. Find the mass of the triangular lamina with vertices for
the density .
a. 139,968k
b. 279,946k
c. 139,958k
d. 139,973k
e. 279,936k
____ 7. Find the mass of the lamina bounded by the graphs of the equations
for the density .
a.
b.
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852 Chapter 14: Multiple Integration
c.
d.
e.
____ 8. Find the center of mass of the lamina bounded by the graphs of the equations
for the density .
a.
b.
c.
d.
e.
____ 9. Find the center of mass of the lamina bounded by the graphs of the equations
for the density .
a.
b.
c.
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14.4 Center of Mass and Moments of Inertia 853
d.
e.
____ 10. Find the mass of the lamina bounded by the graphs of the equations
for the density .
a.
b.
c.
d.
e.
____ 11. Find the center of mass of the lamina bounded by the graphs of the equations
for the density .
a.
b.
c.
d.
e.
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854 Chapter 14: Multiple Integration
____ 12. Find the mass and center of mass of the lamina bounded by the graphs of the
equations given below for the given density.
a.
b.
c.
d.
e.
____ 13. Find the mass of the lamina bounded by the graphs of the equations
for the density .
a.
b.
c.
d.
e.
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14.4 Center of Mass and Moments of Inertia 855
____ 14. Set up and evaluate a double integral required to find the moment of inertia, I, about
the given line, of the lamina bounded by the graphs of the following equations. Use a computer
algebra system to evaluate the double integral.
a.
b.
c.
d.
e.
____ 15. Set up the double integral required to find the moment of inertia I, about the line
of the lamina bounded by the graphs of the equations for the density
. Use a computer algebra system to evaluate the double integral.
a.
b.
c.
d.
e.
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856 Chapter 14: Multiple Integration
____ 16. Determine the location of the horizontal axis for figure (b) at which a vertical gate
in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see
figure (a)). The model for is where is the y-coordinate of the centroid of the gate,
is the moment of inertia of the gate about the line , h is the depth of the centroid below the
surface, and A is the area of the gate.
a.
b.
c.
d.
e.
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14.4 Center of Mass and Moments of Inertia 857
____ 17. Determine the location of the horizontal axis for figure (b) at which a vertical gate
in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see
figure (a)). The model for is where is the y-coordinate of the centroid of the gate,
is the moment of inertia of the gate about the line , h is the depth of the centroid below the
surface, and A is the area of the gate.
a.
b.
c.
d.
e.
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858 Chapter 14: Multiple Integration
14.4 Center of Mass and Moments of Inertia
Answer Section
MULTIPLE CHOICE

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