Applications: Centroid, Work, and Moment of Inertia — Engineering Board Exam Practice Questions
24 free engineering board exam reviewer questions on Applications: Centroid, Work, and Moment of Inertia (Integral Calculus), each with the correct answer and a worked solution.
- Find the x-coordinate of the centroid of the region bounded by y=x2, y=0, x=0, and x=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…
- 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…
- 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.
- Find the moment of inertia about the y-axis of the region bounded by y=x2, x=0, x=2, and the x-axis.
- Find the y-coordinate of the centroid of the region bounded by y=sqrt(x), y=0, and x=4.
- 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.
- 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?
- 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…
- 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…
- A hemispherical tank of radius 3 m, with its flat face on top, is full of water. How much work, in kilojoules, is needed to pump all the…
- A 40-m cable weighing 2.5 kg per meter hangs from the top of a building with a 50-kg load at its lower end. How much work, in kilojoules…
- The region bounded by y=x2, y=9, and the y-axis is revolved about the y-axis to form a solid paraboloid. How far is its centroid from the…
- Find the moment of inertia about the y-axis of the region bounded by y=sqrt(x), x=4, and the x-axis.
- Find the moment of inertia about the x-axis of the region bounded by y=sqrt(x), x=4, and the x-axis.
- Find the y-coordinate of the centroid of the region bounded by y= x, 0≤ x≤π, and the x-axis.
- Find the y-coordinate of the centroid of the region bounded by y=4-x2 and the x-axis.
- Find the distance of the centroid of a quarter-circular area of radius 6 from either straight edge.
- A variable force F(x)=6x2+4x newtons acts along the x-axis. How much work, in joules, is done in moving an object from x=1 m to x=4 m?
- A vertical circular gate 2 m in diameter has its center 5 m below the water surface. Find the hydrostatic force on the gate, in…
- A vertical rectangular gate 4 m wide has its top edge 2 m and its bottom edge 6 m below the water surface. Find the hydrostatic force on…
- A spring has a natural length of 0.30 m, and a force of 40 N holds it stretched 0.10 m beyond natural length. How much work, in joules, is…
- Using integration, find the moment of inertia of a triangle with base 8 and height 6 about its base.
- Find the y-coordinate of the centroid of the region bounded by y=x and y=x2.