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Find the Center of gravity
Asked by sahilsah9211 | 21 Jun, 2023, 01:58: PM
Centre of gravities of semi-circular segment, circular segment and triangle are show in the following figure.
For a semi circular segment , centre of gravity is at symmetry axis and at a distance (2/3)R from diameter , where R is radius of semi-circle.

For a circular segment , centre of gravity is at symmetry axis and at a distance (2/3)R from centre of curvature , where R is radius of semi-circle.

For a triangle , centre of gravity is at the median of triangle and at a distance (1/3)h from base .

The given shape can be divided into six areas each having a standard shape like semi-circle, circular segment and triangle as shown below
Area A1 is  semi-circle of radius 4m . Area A2 and A3 are circular segment of radius 4 m .
Area A4 is isoceless triangle of height 3 m and base 6m. Area A5 is isoceless triangle of height 4 m and base 6 m.

Area A6 is cut-out portion from the given shape which is a semicircle of radius 2m.

As shown in figure , given shape is symmetrically placed on y-axis . Hence x-coordinate of centre of gravity is zero.

Y-coordinate of center of gravity Y is calculated from the following equation.

.........................(1)

Where A1 , A2 , .......A5 and A6 are respective areas of parts and y, y2, ............y5  and y6 are
y-coordinates of centre of gravity of respective part.

AT is total area.

Total area Ais

By substituting relevant values in eqn.(1), we get y-coordinate of centre of gravity as
Answered by Thiyagarajan K | 23 Jun, 2023, 12:22: AM

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