Engineering Board Exam Reviewer · Applications: Centroid, Work, and Moment of Inertia · medium

Find the y-coordinate of the centroid of the region bounded by y=x and y=x2.

  1. 1/2
  2. 3/5
  3. 2/5
  4. 1/5

Answer

C. 2/5

Solution

A= 01(x-x2)dx= 16. y= 1A 01 12≤ft(x2-x4 )dx=6· 12≤ft( 13- 15 )= 25.

More Applications: Centroid, Work, and Moment of Inertia questions

  1. Find the x-coordinate of the centroid of the region bounded by y=x2, y=0, x=0, and x=2.
  2. A spring requires a force of 20 N to stretch it 0.1 m beyond its natural length. Using Hooke's Law, find the work done in stretching it…
  3. A cylindrical tank of radius 2 m and height 5 m, full of water (unit weight 9810 N/m3), is to be pumped empty from the top. Find the work…
  4. Using the Theorem of Pappus, find the volume of the torus generated by revolving a circle of area 4π about an axis 6 units from its center.
  5. Find the moment of inertia about the y-axis of the region bounded by y=x2, x=0, x=2, and the x-axis.
  6. Find the y-coordinate of the centroid of the region bounded by y=sqrt(x), y=0, and x=4.
  7. A 4-m rod has linear density (x)=3x kg/m, where x is measured from the left end. Find its moment of inertia about the left end, in kg·m2.
  8. A 6-m rod has linear density (x)=2+x kg/m, where x is measured from one end. How far from that end is the rod's center of mass, in meters?
  9. A vertical triangular plate has its apex 2 m below the water surface and its horizontal base, 4 m long, at a depth of 5 m. Find the…
  10. A conical tank with its vertex pointing down is 6 m deep and has a top radius of 3 m. It is full of water. How much work, in kilojoules…

All Applications: Centroid, Work, and Moment of Inertia questions