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18001022727You might have tried balancing a ruler or even a book on your finger. Ever wondered what makes this possible or what so special about the point that lets you balance an entire book on one finger? The reason for this lies behind the concept of centre of gravity.
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Centre of gravity is an imaginary point.The centre of gravity is a hypothetical point where the whole weight of the object is concentrated, where the whole weight of the object acts. We can also define the centre of gravity as a point about which gravitational torque comes out to be zero. The point of centre of gravity is of great application in predicting the behaviour of bodies. The centre of gravity finds applications in explaining the behaviour of the bodies when acted upon by gravitational forces.
The image shows the behaviour of a drum under gravitational force. In image A and C, since the drum is supported at the point of centre of gravity, no gravitational torque occurs on the drum. Whereas drum in image B and D, gravitational torque tries to bring the drum to a more stable position.
Centre of gravity is mostly affected by the shape and composition of the objects. In many engineering applications, the concept of centre of gravity plays an important role in the stability of the objects. For example the lower portion of the ships are generally filled with water or weights are added to keep the ships stable in thunderstorms. Also for racing cars, the centre of gravity is kept as low as possible to provide stability at the higher speeds and prevent their rolling sideways.
Centre of mass 
Centre of gravity 
Point at which the entire mass of the body is supposed to be concentrated. 
Fixed point at which the entire weight of the body acts. 
Centre of mass of a body is used to study the motion of the whole body 
Centre of gravity is generally used to study the stability of a body. 
Centre of mass depends upon mass distribution. 
Centre of mass depends upon mass distribution and the gravitational field acting upon it. 
In case of small and symmetrical bodies or when the gravitational field is uniform, the the centre of mass coincides with the centre of gravity. 
In case of extended, nonsymmetrical bodies and when the gravitational field is non uniform, the centre of gravity does not coincide with the centre of mass. 
Since mass in general is not uniformly distributed in an object, determining the centre of gravity becomes complicated. The general case requires use of calculus which is beyond the scope of the topic. If the mass becomes uniformly distributed, the problem becomes greatly simplified.
For uniformly distributed mass objects, centre of gravity can be found using the following methods:
Suspending the plate given in the figure by attaching a cord to point A and then by attaching the cord at point C, the centre of gravity of the plate can be located.
Suspending a plate by means of a cord attached to the points A and C, the centre of gravity of the plate can be calculated as follows:
For a triangular metal plate shown in the figure, the centre of gravity is calculated by taking the sum of the moments of the weights of the particles which make up the triangle. This equals to the weight W Multiplying this with the unknown distances from sides AC, CB and AB to the centre of gravity G we get the position of G relative to the sides.
Shape of body 
Position of CG 
Thin Uniform Bar 
middle point of the bar 
Circular Ring 
centre of the ring 
Circular Disk 
centre of the disk 
Sphere, Hollow Sphere, Annular Disk 
at its centre 
Cubical or Rectangular Block 
point of intersection of the diagonals 
Triangular Lamina 
point of intersection of the medians 
Square Lamina, Parallelogram and Rectangular Lamina 
point of intersection of the diagonals 
Cylinder 
middle point of the axis 
Q1. An uniform rod of mass 3 kg is hinged at the wall and connected through a light string as shown in the figure. Find the moment due to the weight of the rod about point O.
A. Given, mass of the rod, m = 3 kg
Q2. Four homogeneous bricks, each of length L = 4m, are arranged as shown in the figure. Each bricks is displaced in displaced with respect to the one in contact by L/8 Each brick is placed in contact with one another at a distance of L/8 from each other. Find the x coordinate of the centre of gravity relative to origin O.
A.
Length of each brick, L = 4m, Let the mass of each brick be m kg.
Initially all four bricks have their COG at L/2 =2 from the xaxis.
After displacing the bricks, coordinates relative to origin O :
Q3. A square plate of uniform thickness and density is bent along M_{1}M_{2} till corner C coincides with centre C' as shown in Figures . Determine its centre of gravity.
A. Let w be the uniform weight of the plate per unit area. The entire plate after it is bent can be considered to be made up of three parts.
(1) W_{1} = weight corresponding to a square plate OACB
= (36w) at location (3,3)
(2) W_{2} = weight corresponding to overlapped portion M_{1}CM_{2}
= (4.5w) at location (4,4)
(3)  W_{3} = portion (M_{1}CM_{2}) which is removed
= ( 4.5w) at location (5,3)
Resultant weight, W = W_{1 }+ W_{2 }+ W_{3 }= 36w + 4.5w + (4.5w) = 36w
S. no 
W_{i} 
x_{i} 
W_{i}x_{i} 
Y_{i} 
W_{i}Y_{i} 
1 

3 
108w 
3 
108w 
2 

4 
18w 
4 
108w 
3 

5 
 22.5w 
5 
 22.5w 



ΣW_{i}x_{i} = 103.5w 

ΣW_{i}x_{i} = 103.5w 
Q4. Determine the C.G. of a wire of uniform crosssection bent into shape of a semicircle as shown in figure
A.
Length of the wire, L = na where a = radius of semicircle
Question 1. Why is the centre of gravity important?
Answer. The Centre of gravity vastly simplifies calculations involving gravitation and dynamics to treat the mass of an object as if it is concentrated at one point.
Question 2. How does centre of gravity affect stability?
Answer. The position of the centre of gravity of an object affects its stability. The lower the centre of gravity (G) is, the more stable the object. The higher it is, the more likely the object is to topple over if it is pushed.
Question 3. Why is the centre of gravity of symmetrical objects always positioned on the axis of symmetry?
Answer. For a symmetrical object, the weight of each subpart will be balanced by the subpart’s weight on the opposite side of the axis. Therefore the moment comes out to be zero around the axis of symmetry and hence the centre of gravity falls on it.
Question 4. How does centre of gravity change in a person?
Answer. While walking or bending, the centre of gravity changes so that the person remains stable.