Unit 3 - Practice Quiz

1 What is the term used to describe the geometric center of an area or a line?

2 The point through which the entire weight of a body acts is called its:

3 Where does the centroid of a rectangle of width and height lie with respect to its base?

4 Where does the centroid of a right-angled triangle of height lie from its base?

5 What is the distance of the centroid of a semicircle of radius from its diametric base?

6 How is the x-coordinate of the centroid () of a composite area calculated?

7 The first moment of an area about its own centroidal axis is always:

8 Moment of inertia of an area is also known as:

9 What is the SI unit for the moment of inertia of a plane area?

10 What is the moment of inertia of a rectangular section of width and depth about its centroidal axis parallel to the width?

11 What is the moment of inertia of a solid circular section of diameter about its centroidal diameter?

12 Which theorem states that for a plane lamina?

13 The parallel axis theorem for area moment of inertia is mathematically expressed as:

14 What is the SI unit for mass moment of inertia?

15 If a composite body has an axis of symmetry, its centroid:

16 The polar moment of inertia is the moment of inertia about which axis?

17 The first moment of area represents:

18 What is the moment of inertia of a rectangle of base and height about its base?

19 For a thin uniform rectangular plate of mass , width and depth , the mass moment of inertia about the centroidal axis parallel to width is:

20 Where is the centroid of a quarter-circle of radius located with respect to its bounding straight edges?

21 What is the location of the centroid of a semicircular area of radius from its diametral base?

22 What is the centroidal distance for a right-angled triangle with base and height , measured from the right angle?

23 The first moment of an area about any centroidal axis is always:

24 The moment of inertia of a rectangular section of width and depth about its centroidal axis parallel to the width is:

25 According to the parallel axis theorem, the moment of inertia about an axis parallel to the centroidal axis is given by:

26 The perpendicular axis theorem is applicable only to:

27 What is the moment of inertia of a circular section of diameter about its centroidal diametral axis?

28 The polar moment of inertia of a circular section of radius is:

29 A composite area consists of a square of side and a semicircle of radius attached to one of its sides. What is the total area used to calculate its centroid?

30 For a quarter circular arc of radius , the centroid from the center along the axis of symmetry is at a distance of:

31 Which of the following bodies will have its center of gravity outside its physical material?

32 To find the moment of inertia of an I-section about its centroidal X-axis, which theorem is most commonly used for its flanges?

33 The moment of inertia of a triangle of base and height about its base is:

34 The mass moment of inertia of a thin rectangular plate of mass , sides and , about an axis through its center and perpendicular to its plane is:

35 If the first moment of an area about the x-axis is and about the y-axis is , the coordinates of the centroid are:

36 When a circular hole of area is punched out from a larger circular plate of area , the x-coordinate of the new centroid is given by:

37 The center of gravity of a solid right circular cone of height lies on its axis of symmetry at a distance from the base equal to:

38 What is the radius of gyration of a rectangular section of width and depth about its centroidal axis parallel to the width?

39 For a thin circular plate of mass and radius , what is its mass moment of inertia about a diametral axis?

40 A uniform wire is bent into the shape of a semicircle of radius . What is the distance of its centroid from the center of the semicircle?

41 A semi-circular arc of radius is located in the first quadrant with its center at the origin. What is the -coordinate of its centroid?

42 The polar moment of inertia of a solid circular section of diameter is given by:

43 Consider a composite wire formed by a straight segment of length along the x-axis and a quarter-circular arc of radius lying in the first quadrant, tangent to the straight segment at the origin. What is the x-coordinate of the centroid of this composite wire?

44 The moment of inertia of a rectangular area of base and height about an axis passing through its base is:

45 A solid right circular cone of base radius and height is hollowed out by a cylindrical hole of radius () along its central axis. The z-coordinate of the center of gravity of the remaining solid, measured from the base, depends non-linearly on which ratio?

46 For a thin rectangular plate of mass , width , and length , the mass moment of inertia about an axis perpendicular to the plate and passing through one of its corners is:

47 An I-section has overall depth , flange width , flange thickness , and web thickness . The moment of inertia about the strong axis (centroidal x-axis) is correctly expressed as:

48 A parabolic spandrel is bounded by the x-axis, the line , and the parabola . If the maximum height is at , what is the first moment of area about the y-axis?

49 What is the centroidal y-coordinate () of the area bounded by the curves and the x-axis for ?

50 Determine the moment of inertia of a quarter-circle of radius about its centroidal axis parallel to the straight edge.

51 A thin wire is bent to form a semi-circle of radius and a straight line of length connecting the ends of the semi-circle. What is the distance of the centroid of this closed loop from the straight wire?

52 A hollow rectangular section has external dimensions and internal dimensions . If the section is subjected to rotation such that the principal axes are inclined at to the centroidal axes, what condition must hold true?

53 The polar moment of inertia of an equilateral triangle of side about its centroid is:

54 Consider a thin elliptical plate of mass , with semi-major axis and semi-minor axis . The mass moment of inertia about the centroidal axis perpendicular to the plate is:

55 A hemisphere of radius and a right circular cone of base radius and height are joined at their bases. For the center of gravity of the combined solid to lie exactly at the center of the common base, what must be the relationship between and ?

56 The first moment of the area of a semi-ellipse (bounded by the minor axis) with semi-major axis and semi-minor axis , evaluated about the minor axis, is:

57 The area between , the y-axis, the x-axis, and has a centroid x-coordinate given by:

58 For a T-section with uniform thickness , flange width , and overall depth , the distance of the centroid from the top fiber is approximately (assuming ):

59 Which of the following statements about the product of inertia is ALWAYS true?

60 A thin circular disk of mass and radius has a circular hole of radius cut out. The hole is tangent to the center of the disk. What is the mass moment of inertia of the remaining disk about an axis passing through its center of gravity and perpendicular to its plane?