Unit 1: Experimental study of C.G location - Practice Quiz

1 What does C.G. stand for in the study of a plane lamina?

2 Where is the C.G. of a uniform rectangular lamina located?

3 Where is the C.G. of a uniform circular lamina located?

4 Which property helps predict the C.G. of a uniform symmetrical lamina?

5 Where is the C.G. of a uniform square lamina?

6 What is commonly attached to the suspension point when locating C.G. experimentally?

7 When a lamina hangs freely, where does its C.G. lie relative to the suspension point?

8 For a uniform triangular lamina, the C.G. is located at the intersection of its:

9 A uniform lamina has two axes of symmetry. Where should its C.G. be?

10 What assumption is usually made about a lamina in a simple C.G. experiment?

11 Which method is commonly used to find the C.G. of an irregular lamina?

12 How many suspension points are normally sufficient to locate the C.G. of an irregular lamina?

13 What should be done after an irregular lamina stops swinging freely?

14 What identifies the C.G. after an irregular lamina is suspended from two points?

15 Why is an irregular lamina suspended from a second point?

16 Which instrument provides a reliable vertical reference in the suspension experiment?

17 Why should the lamina be allowed to stop swinging before a line is drawn?

18 How can the experimentally found C.G. of an irregular lamina be checked?

19 What may happen if the suspension points are chosen very close together?

20 What does the plumb bob do in a C.G. experiment?

21 A uniform rectangular lamina is suspended from one corner, and a vertical line is drawn using a plumb bob. What must be done next to locate its C.G experimentally?

22 A uniform rectangular sheet measures . Taking one corner as the origin, where should its experimentally determined C.G be located?

23 A uniform square lamina is suspended from its upper-left corner. Which path will the plumb line follow across the lamina?

24 An experimentally drawn vertical line on a uniform circular disc misses the center marked using its diameter by several millimetres. What is the most likely experimental cause?

25 A uniform isosceles triangular lamina has only its vertical axis of symmetry marked. What can be concluded about its C.G before performing the suspension experiment?

26 Two vertical lines obtained by suspending a uniform rectangular lamina intersect away from the intersection of its diagonals. Which conclusion is most reasonable?

27 A uniform equilateral triangular lamina has a height of . How far above its base should the experimentally found C.G lie?

28 Why is balancing a symmetrical lamina on a narrow knife edge useful after locating its C.G by suspension?

29 A uniform circular lamina is suspended successively from three points on its rim. Ideally, how should the three plumb lines appear?

30 A uniform rectangular lamina balances horizontally when supported at its center. A small equal-sided piece is cut from the left edge only. What will happen to the C.G?

31 An irregular cardboard lamina is suspended from point . After it settles, where must its C.G lie?

32 For an irregular lamina, why should two suspension points be chosen well apart rather than very close together?

33 Two plumb lines drawn on an irregular lamina are represented by and . What are the coordinates of the experimental C.G?

34 Three suspension lines on an irregular lamina form a very small triangle instead of meeting at one point. What is the best estimate of the C.G?

35 A small lump of clay is attached to the right side of an irregular lamina after its C.G has been marked. Where will the new C.G generally move?

36 An irregular crescent-shaped lamina is tested by suspension. The plumb lines intersect in an empty region inside the crescent's curve. Is this result physically possible?

37 An irregular lamina is rotated before being suspended from the same body-fixed hole. How does its C.G position relative to the lamina change?

38 A student holds the plumb string slightly sideways while marking a line on an irregular lamina. What effect is most likely?

39 Two small masses form an unsymmetrical model: is at and is at . Where is their combined C.G?

40 An irregular lamina balances on a pencil tip placed at the intersection of its suspension lines. What does this observation confirm?

41 Three equal-precision suspension trials on a uniform symmetrical lamina produce the traced lines , , and . Using the point that minimizes the sum of squared perpendicular distances to the lines, what is the best estimate of the C.G.?

42 A rectangular lamina is geometrically symmetric about both centerlines, but its measured C.G. does not lie on the vertical centerline. Which conclusion is most scientifically justified?

43 A uniform isosceles triangular lamina of altitude is suspended in two different orientations. Where should the traced plumb lines intersect relative to the base?

44 For a uniform semicircular lamina of radius , an experiment measures the C.G. on the symmetry axis. Which theoretical distance from the diameter should be used for comparison?

45 A uniform annular lamina is suspended from several points. All plumb lines intersect at the center of its empty hole. How should this observation be interpreted?

46 A symmetric plate of mass has its C.G. at the origin. A small mass is attached at . Where should a repeated suspension experiment locate the new C.G.?

47 A rectangular lamina occupies and , but its areal density is , where . What C.G. should the suspension experiment reveal?

48 A uniform symmetric lamina is first suspended from a point lying exactly on its only symmetry axis. The traced plumb line coincides with that axis. Why is a second suspension from an off-axis point still useful?

49 Each traced plumb line has the same small perpendicular-position uncertainty. Which pair of suspension lines generally gives the smallest uncertainty in their intersection?

50 Several suspension lines for a symmetric lamina form a small cluster rather than one exact intersection, while one line misses the cluster widely. What is the best experimental response?

51 An L-shaped uniform lamina is formed from a square by removing the upper-right square. Taking the original square's lower-left corner as the origin, where should suspension lines intersect?

52 A uniform plate has a circular hole of radius centered at . Which predicted C.G. should be compared with the plumb-line result?

53 A uniform triangular lamina has vertices , , and . At which point should three accurately traced suspension lines concur?

54 For a strongly concave uniform lamina, the extensions of the suspension lines intersect in an open region outside the lamina. Which assessment is correct?

55 For an irregular lamina, equal-precision suspension trials produce , , and . Why is simply choosing the intersection of the first two lines inferior to a least-squares estimate?

56 An irregular plate of mass has unknown C.G. coordinate . After a mass is attached at coordinate , suspension trials measure the combined C.G. at . Which expression recovers ?

57 In body-fixed coordinates, an irregular lamina is suspended at . The downward plumb-line direction is the unit vector . Which locus correctly represents possible C.G. positions from this trial?

58 A rectangular lamina consists of a left region with areal density and a right region with density . Using the lower-left corner as the origin, where should the C.G. be measured?

59 Accurate suspension lines for a large irregular lamina fail to concur, and the discrepancy changes systematically with the lamina's orientation in a region having a strong gravitational gradient. What assumption of the standard method is most directly violated?

60 A uniform irregular lamina is enlarged geometrically by a scale factor while preserving thickness and density. Coordinates are measured from corresponding origins. How should its experimentally determined C.G. coordinates change?