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. 
|
|
|
2.
|
Find the center of mass of the point masses lying on the
x-axis. 
|
|
|
3.
|
Find the center of mass of the point masses lying on the
x-axis. 
|
|
|
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.
|
|
|
7.
|
Find the center of mass of the given system of point masses.
|
|
|
8.
|
Find the center of mass of the given system of point masses.
|
|
|
9.
|
Find  for the lamina of uniform density  bounded by the graphs of the equations  .
|
|
|
10.
|
Find  for the lamina of uniform density  bounded by the graphs of the equations  .
|
|
|
11.
|
Find Mx, My, and  for the
lamina of uniform density  bounded by the graphs of the equations  .
|
|
|
12.
|
Find Mx, My, and  for the
lamina of uniform density  bounded by the graphs of the equations  .
|
|
|
13.
|
Find  for the lamina of uniform density  bounded by the graphs of the equations  .
|
|
|
14.
|
Find  for the lamina of uniform density  bounded by the graphs of the equations  .
|
|
|
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  .)  .
|
|
|
16.
|
Find the volume of the solid generated by rotating the circle 
about the y-axis.
|
|
|
17.
|
Find the volume of the solid generated by rotating the circle 
about the x-axis.
|
|
|
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 |
|