Supplement to High school physical science . nce the centre of gravity of the parallelogramis at G, the point of intersection of EF and HK, thediameters of the To find the Centre of Gravity of a Triangular Lamina. Let ABC (Fig. 20) be the triangular lamina, and letthe middle points of AB, BC and CAbe D, E and F respectively. Consider the lamina to be madeup of a series of very thin parallelrods such as LM, each parallel to BC. The centre of gravity of each ofthese rods is at its middle point g;but the median AE bisects all suchBrods; therefore the centre of gravityof each rod
Supplement to High school physical science . nce the centre of gravity of the parallelogramis at G, the point of intersection of EF and HK, thediameters of the To find the Centre of Gravity of a Triangular Lamina. Let ABC (Fig. 20) be the triangular lamina, and letthe middle points of AB, BC and CAbe D, E and F respectively. Consider the lamina to be madeup of a series of very thin parallelrods such as LM, each parallel to BC. The centre of gravity of each ofthese rods is at its middle point g;but the median AE bisects all suchBrods; therefore the centre of gravityof each rod lies in AE; hence the centre of gravity ofthe lamina lies in AE. In a similar manner the lamina may be regarded asmade up of a series of rods parallel to AB or AC, and itscentre of gravity shown to lie in the medians CD or BF. Hence the centre of gravity of the triangular laminais at G, the point where the medians intersect, that is inthe line joining the middle point of any side to theopposite vertex at one-third its length from that EXERCISE X. 1. An isosceles triangle has its equal sides of length 5 cm. and itsbase of length 6 cm. Find the distance of the centre of gravityfrom each of the angular points. 2. If the angular points of one triangle lie at the middle points 56 SUPPLEMENT TO HIGH SCHOOL PHYSICAL SCIENCE. of the sides of another, show that the centre of gravity of the twoare coincident. 3. The equal sides of an isosceles triangle are 10 feet, and the baseis 16 feet in length. Find the distance of its centre of gravity fromeach of the sides. 4. The sides of a triangle are 3, 4, and 5 feet in length. Findthe distance of the centre of gravity from each side. 5. The sides of a triangular lamina are 6, 8, and 10 feet in the distance of the centre of gravity from each of its angularpoints. 6. The sides AB, AC of a triangle ABC, right-angled at A, arerespectively 18 and 12 inches long. Find the distance of the centreof gravity from C. 7. Show that the c
Size: 1433px × 1744px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1890, bookpublis, booksubjectmechanics
