Larson_Calculus_10e ch07sec06
MULTIPLE CHOICE
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.
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
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.
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.
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.
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.
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.
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