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Center of Gravity and Centroid
Multiple Choice

1 .      

Locate the centroid of the parabolic area. 



2 .      

Locate the centroid of the exparabolic segment of area. 



3 .      

Locate the centroid of the shaded area. 



4 .      

Locate the center of gravity of the volume generated by revolving the shaded area about the z axis. The material is homogeneous. 



5 .      

Locate the center of gravity of the homogeneous "bell-shaped" volume formed by revolving the shaded area about the y axis. 



6 .      

The truss is made from seven members, each having a mass of 6 kg/m. Locate the position (,) of the center of mass. Neglect the mass of the gusset plates at the joints. 



7 .      

Determine the distance to the centroid axis of the beam's cross-sectional area. Neglect the size of the corner welds at A and B for the calculation. 



8 .      

Determine the distance to the centroidal axis of the beam's cross-sectional area. 



9 .      

Locate the centroid of the cross-sectional area of the beam constructed from a plate, channel and four angles. Handbook values for the areas and centroids Cc and Ca of the channel and one of the angles are listed. Neglect the size of all the rivet heads, R, for the calculation. 



10 .      

Using integration, compute both the area and the centroidal distance of the shaded region. Then, using the second theorem of Pappus-Guldinus, compute the volume of the solid generated by revolving the shaded area about the aa axis. 



11 .      

Determine the volume of concrete needed to construct the circular curb. 



12 .      

Determine the approximate amount of paint needed to cover the surface of the water storage tank. Assume that a liter of paint covers 2.5 m2. Also, what is the total inside volume of the tank. 



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