The document defines key terms related to the properties of surfaces and solids: 1) The centroid is the point where the total area of a plane figure is assumed to be concentrated. 2) The center of gravity is the point through which the entire weight of a body acts. 3) Pappus-Guldinus theorem relates the surface area of a solid of revolution to the length of the generating curve and the distance traveled by its centroid.

1. Unit- 3(Properties of Surfaces and Solids) 2marks
1. Define centroid.
The centroid is defined as the point at which the total area of plane figures namely
rectangle, square, triangle circle etc. It is assumed to be concentrated.
2. Define centre gravity.
The centre of gravity of a body may be defined as the point through which the entire
weight of the body acts. Denoted by CG or G
3. State Pappus-Guldinus theorem for finding surface area.
It states that “The area of surface of revolution is equal to the product of the length of the
generating curve and the distance travelled by the centroid of the generating curve while generating
that surface”.
4. State Pappus-Guldinus theorem for finding volume.
It states that “the volume of a body of revolution is obtained from the product of the generating
area and the distance travelled by the centroid of the area, while the body is being generated”.
4. Define moment of inertia.
A quantity expressing a body's tendency to resist angular acceleration, which is the sum
of the products of the mass of each particle in the body with the square of its distance from the
axis of rotation
5. Define radius of gyration.
Radius of gyration is defined about an axis. The elemental parts of an area are
concentrated at a radius from an axis such that the area moment of inertia about the same axis is
same.
6. What is polar moment of inertia?
The area moment of inertia about an axis perpendicular to the plane of an area is called
polar moment of inertia.
Ip= Ixx + Iyy

2. 7. When will the product of inertia will be zero?
The product of inertia of a symmetrical area about one or two axes of symmetry must
be zero.
8. Define parallel axis theorem.
The theorem of parallel axis states that the moment of inertia of a body about an axis
parallel to an axis passing through the centre of mass is equal to the sum of the moment of inertia
of body about an axis passing through centre of mass and product of mass and square of the
distance between the two axes.
Io= Ic+ mh2
9. Define perpendicular axis theorem.
This theorem states that the moment of inertia of a planar body about an axis
perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular
axes concurrent with the perpendicular axis and lying in the plane of the body.
Ioz= Iox + Ioy
10. Define mass moment of inertia.
The property which measures the resistance of a body to angular acceleration is the mass
moment of inertia of the body. The larger the Mass Moment of Inertia the smaller the angular
acceleration about that axis for a given torque.
Note: Simple Problems may asked by using formulas or formulas may asked for simple
sections.