M.P.KEDARNATH / Asst Prof - Mechanical Page 1

MAHALAKSHMI

ENGINEERING COLLEGE

TIRUCHIRAPPALLI – 621213

Sub Code: GE 6253 Semester: II

Subject: ENGINEERING MECHANICS Unit – III: PROPERTIES OF SURFACES

AND SOLIDS

PART A

1. Distinguish between centroid and centre of gravity. (AU DEC’09 ,DEC’12)

2. State parallel axis theorem with simple sketch. (AU DEC’09, DEC’10, JUN’12)

3. Define radius of gyration with respect to x-axis of an area.(AU JUN’09, DEC’10,JUN’12)

4. Define polar moment of inertia of lamina. (AU DEC’11)

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5. Write the SI units of the mass moment on inertia and of the area moment of inertia of a

lamina. (AU JUN’10)

6. Define first moment of an area about an axis. (AU MAY’11)

7. Define principal axes and principal moment of inertia. (AU MAY’11 , DEC’12)

8. When will the product of inertia of a lamina become zero? (AU JUN’10, DEC’11)

9. State principal axes of inertia? (AU JUN’09)

10. What is meant by moment of inertia of the area?

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PART B

1. Derive from first principles, the second moment of area of a circle about its diametral .

Axis. (AU JUN’10, DEC 12)

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2. For the section shown in figure below, locate the horizontal and vertical centroidal

Axis (AU JUN’12)

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3. Calculate the centroidal polar moment of inertia of a rectangular section with breadth

of 100 mm and height 200 mm. (AU DEC’10,JUN’12)

4. Find the moment of inertia of the shaded area shown in figure about the vertical and

horizontal centroidal axes. The width of the hole is 200 mm. (AU DEC’12, JUN’10)

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5. Derive the expressions for the location of the centroid of a triangular area shown in

Figure, by direct integration. (AU DEC’11, DEC’12)

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6. Locate the centroid of the plane area shown in figure below. (AU DEC’11, DEC’12)

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7. Figure shows a composite area. (AU DEC’11, JUN’ 10)

Find the moments of inertia (second moments of area) about both the centroidal axes.

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8. Derive the expression for the product of inertia of the rectangular area about x and y axes

shown (AU MAY’11,DEC ‘12)

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9. Locate the centroid of the plane area shown in figure below (AU MAY’11)

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10. An area in the form of L section is shown in figure below (AU MAY’11, DEC’12)

Find the moments of Inertia Ixx, Iyy, and Ixy about its centroidal axes. Also

determine the principal moments of inertia.

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11. Derive, from first principle, the second moment of area for the rectangular

area when the axes are as shown below: (AU JUN’10, DEC’12)

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12. Locate the centroid of the area shown in figure below. The dimensions are in mm. (AU JUN’10,DEC 11)

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13. Explain the steps to be followed to find the principal moments of inertia of a given section. How will you find the inclination of the principal axes? (AU JUNE’10,DEC 12)

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14. A rectangular prism is shown in figure. The origin is at the geometric centre of the

prism. The x, y and z-axes pass through the mid points of faces. (AU JUNE’10,DEC’11)

Derive the mass moment of inertia of the prism about the x-axis.

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15. Find the moment of inertia of a section shown in Fig below about the centroidal

Axes.(Dimensions in mm) (AU JUN’09)

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16. Find the polar moment of inertia of a T section shown in Fig 5 about an axis passing

through its centroid. Also find the radius of gyration with respect to the polar

axis. (Dimensions in mm) (AU JUN’09)

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17. Calculate the centroidal moment of inertia of the shaded area shown in figure below. (AU

DEC’09,JUN’12)

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18. Steel forging consists of a 60 x 20 x 20 mm rectangular prism and two cylinders of diameter 20mm and length 30mm as shown in figure below .Determine the moments of inertia of the forging with respect to the coordinate axes, knowing that the density of steel is 7850 Kg/m3 . (AU DEC’09, JUN 10)

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