centroid of cut out sections

1. CENTROID OF CUT OUT SECTIONS

2. CENTER OF GRAVITY
Every particle of a rigid body is attracted by
the earth towards its center.
The force of attraction which is proportional to the mass
of the particle ( F & M) and acts vertically downwards is
called the weight of that particle.
By the laws of compounding of parallel forces, a
point may be found in the body through which the
resultant of all such parallel forces acts. This point
through which the whole weight of the body acts for
all position of the body is called the center of
gravity of the body.

3. The point through which the whole weight of the body acts, for all
position of the body, is called the center of gravity of the body.
The point through which the whole area of the lamina acts, for all
positions of the body, lamina, is called the centroid of the lamina.
Methods of determining Centre of Gravity
The determination of the Centre of gravity of the body
which is essentially the determination of the center of parallel
forces or areas may be done by any one of the following methods.
• By Geometrical methods.
• By methods of moments.
• By integration methods.
• By Graphical methods.

4. Centre of gravity of the body by
Geometrical methods.
The centre of gravity of the uniform thin rod
is at its middle
The centre of gravity of a rectangle or a
parallelogram is at a point where the two
diagonals meet each other. It is also the
middle point of the length and breadth of the
rectangle.
The centre of gravity of a triangle is at a
point, where the three medians meet.
Median is a line, connecting the vertex and
the middle point of the opposite.

5. Center of gravity of solid bodies
The centre of gravity of solid bodies such as hemispheres,
cylinders, right circular cone, etc is found out as in same way
as that as that of plane figures. The only difference, between
the plane figures is that in case of solid bodies, we calculate
volumes instead of areas. The volume of few solid bodies are:
Volume of cylinder:
Volume of hemisphere:
Volume of right circular cone:

6. A solid body formed by joining the base of a right circular cone of height
H to the equal base of right circular cylinder of height h. calculate the
distance of the centre of mass of the solid from its plane face, when
H=120mm and h=30mm.

7. A body consists of a rigth circular solid cone of height 40mm and radius
30mm placed on a solid hemisphere of radius 30mm of the same material.
Find the position of centre of gravity of the body.

8. CENTRE OF GRAVITY OF SECTIONS WITHCUT OUT HOLES
The centre of gravity is found out by considering the main
section, first as a complete one, and then deducting the area of
the cut out hole ie., by taking the area of the cut out hole as
negative.
Centre of gravity

9. A square hole is punched out of circular lamina, the diagonal of the square
being the radius of the circle. Find the centre of gravity of the
remainder if r is the radius of the circle.

10. A circular section of angle 60° is cut from the circle of radius r. determine
the centre of gravity of the remainder