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7.6 Moments, Centers of Mass, and Centroids 431
7.6 Moments, Centers of Mass, and Centroids
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the center of mass of the point masses lying on the x-axis.
a.
b.
c.
d.
e.
____ 2. Find the center of mass of the point masses lying on the x-axis.
a.
b.
c.
d.
e.
432 Chapter 7: Applications of Integration
____ 3. Find the center of mass of the point masses lying on the x-axis.
a.
b.
c.
d.
e.
____ 4. Consider a beam of length feet with a fulcrum x feet from one end as shown in
the figure. Two objects weighing 36 pounds and 108 pounds are placed at opposite ends of the beam.
Find x (the distance between the fulcrum and the object weighing 36 pounds) such that the system is
equilibrium.
a. 10 feet
b. 11 feet
c. 8 feet
d. 9 feet
e. 7 feet
7.6 Moments, Centers of Mass, and Centroids 433
____ 5. Consider a beam of length feet with a fulcrum x feet from one end as shown in
the figure. In order to move a 550-pound object, a person weighing 214 pounds wants to balance it on
the beam. Find x (the distance between the person and the fulcrum) such that the system is
equilibrium. Round your answer to two decimal places.
a. 5.10 feet
b. 3.35 feet
c. 3.45 feet
d. 4.60 feet
e. 3.60 feet
____ 6. Find the center of mass of the given system of point masses.
a.
b.
c.
d.
e.
434 Chapter 7: Applications of Integration
____ 7. Find the center of mass of the given system of point masses.
a.
b.
c.
d.
e.
____ 8. Find the center of mass of the given system of point masses.
a.
b.
c.
d.
e.
7.6 Moments, Centers of Mass, and Centroids 435
____ 9. Find for the lamina of uniform density bounded by the graphs of the
equations .
a.
b.
c.
d.
e.
____ 10. Find for the lamina of uniform density bounded by the graphs of the equations
.
a.
b.
c.
d.
e.
____ 11. Find Mx, My, and for the lamina of uniform density bounded by the graphs
of the equations .
a.
b.
436 Chapter 7: Applications of Integration
c.
d.
e.
____ 12. Find Mx, My, and for the lamina of uniform density bounded by the graphs
of the equations .
a.
b.
c.
d.
e.
____ 13. Find for the lamina of uniform density bounded by the graphs of the
equations .
a.
b.
c.
7.6 Moments, Centers of Mass, and Centroids 437
d.
e.
____ 14. Find
for the lamina of uniform density bounded by the graphs of the equations
.
a.
b.
c.
d.
e.
____ 15. Set up and evaluate integrals for finding the moment about the y-axis for the region
bounded by the graphs of the equations. (Assume .)
.
a.
b.
c.
d.
e.
438 Chapter 7: Applications of Integration
____ 16. Find the volume of the solid generated by rotating the circle
about the y-axis.
a.
b.
c.
d.
e.
____ 17. Find the volume of the solid generated by rotating the circle
about the x-axis.
a.
b.
c.
d.
e.
____ 18. Use the Theorem of Pappus to find the volume of the solid formed by revolving the
region bounded by the graphs of about the x-axis. Round your answer to two
decimal places.
a. 1809.56
b. 2787.64
c. 2094.40
d. 3141.59
e. 3619.11
7.6 Moments, Centers of Mass, and Centroids 439
7.6 Moments, Centers of Mass, and Centroids
Answer Section
