Centre of Gravity of a Body

part.For a compound body, the centre of gravity is the mid-point of the centres of gravity of its components.Discussion:Compare the experimental results of the centre of gravity of the regular shapes with the theoretical values. Explain briefly.ShapeTheoretical ValuesCircleCircumcentreRectangleIntersections of DiagonalsIsosceles TriangleIntersections of MediansTable 1 – Theoretical Values of Centre of Gravity for Different ShapesThe theoretical value of L-shaped lamina is illustrated as follow:    Figure 1Figure 2Figure 3Figure 4Divide the shape into two rectangles, as shown in Figure 2. A dotted line is drawn by joining the centre of gravities of separated rectangles, which are the intersections of the diagonals. Then the center of gravity of the shape must lie on the dotted line. Similarly, as shown in Figure 3, another dotted line, where the centre of gravity must lie on it, can be found. As the center of gravity of the shape must lie along the two dotted lines, it is obvious that it is at the intersection of these two lines, as shown in Figure 4.It is assumed that the densities of the laminas are uniform when determining their theoretical values.For circle, rectangle and isosceles triangle, the experimental results are consistent with the theoretical values. However, for L-shaped cardboard, by comparing the experimental results (as shown in Figure 4), there is a very small deviation between the experimental and theoretical values. This is due to the error in marking the intersection points of the vertical string and the edges of the cardboard on the cardboard.Is it necessary for the centre of gravity to be situated inside the body?It is unnecessary since in the case of L-shaped cardboard, the centre of gravity lies outside the body.Comment the case for the irregular shapes.It is observed that the centre of gravity of the nut-shaped board is located at the lower part which is more massive. Since it is in irregular shape, it is difficult to obtain theoretical value, i.e. its centroid. Therefore, its centre of gravity can only be determined by experimental methods.Discuss the centre of gravity of a compound body made of regular shapes.After combining two shapes, the compound body is still reflectionally symmetric, so the centre of gravity of the compound body lies on the axis of symmetry.Besides, experimental result reveals that the centre of gravity is closer to the more massive part as proved in part 6. Then by comparing with the results of rectangle and L-shaped laminas, it is easy to observe that the centre of gravity of a compound body is the mid-point of the centres of gravity of the components.State the sources of error and suggest improvements for the experiment.When marking the intersection points of the vertical string and the edges of the cardboard on the cardboard, the markings may deviate from the original position.The density may not be uniform throughout the lamina.OthersHere is the proof showing why the centre of gravity lies on the more massive part in an irregular body:Let G be the centre of gravity of the object, m1 and m2 be the centre of gravity of the upper and lower part of the object, where m1 < m2. They are distanced from each other by length d. Besides, x is the distance between m1 and G. A simplified diagram is shown on Figure 6.Then ➔ m1 < m2➔ m1 + m2 < 2m2Therefore, G is closer to m2 and the centre of gravity of the object should be lie on the more massive part.Figure 5Figure 6 - End of Report -