#### Topics

1) Define Centre of gravity of a body ?

Centre of gravity of body is defined as appoint of application of the resultant force due to the earth’s attraction on it. The center of gravity is the location around which a body rotates if under no translational forces. If you could balance a body on a point at its center of gravity it would not rotate. The center of gravity for a body can be located by suspending the body from a number of points on its edge the CoG will always be directly under the point of suspension. (Or balancing on a knife edge or equivalent in which case the CoG will be directly above the intersection of the numerous balancing lines).

2) Define stable equilibrium with examples ?

When the center of gravity of a body lies below point of suspension or support, the body is said to be in STABLE EQUILIBRIUM. For example a book lying on a table is in stable equilibrium. A book lying on a horizontal surface is an example of stable equilibrium. If the book is lifted from one edge and then allowed to fall, it will come back to its original position.
Other examples of stable equilibrium are bodies lying on the floor such as chair, table etc. When the book is lifted its center of gravity is raised. The line of action of weight passes through the base of the book. A torque due to weight of the book brings it back to the original position.

3) Define unstable equilibrium with examples ?

When the center of gravity of a body lies above the point of suspension or support, the body is said to be in unstable equilibrium. Pencil standing on its point or a stick in vertically standing position. If thin rod standing vertically is slightly disturbed from its position it will not come back to its original position. This type of equilibrium is called unstable equilibrium, other example of unstable equilibrium are vertically standing cylinder and funnel etc. When the rod is slightly disturbed its center of gravity is lowered. The line of action of its weight lies outside the base of rod. The torque due to weight of the rod toppled it down.

4) Define neutral equilibrium with examples ?

When the center of gravity of a body lies at the point of suspension or support, the body is said to be in neutral equilibrium. Example: rolling ball. If a ball is pushed slightly to roll, it will neither come back to its original nor it will roll forward rather it will remain at rest. This type of equilibrium is called NEUTRAL EQUILIBRIUM. If the ball is rolled, its center of gravity is neither raised nor lowered. This means that its center of gravity is at the same height as before.

5) Derive or Experiment to derive the conditions for stability ?

Stick three pins close together to the bottom of a cork and make the cork stand on the pins (figure (b) shown below). Now try to push or tilt the cork and see what happens. Remove the pins and fix on the cork as shown in figure (b) below. You will notice that in the new arrangement, the base has become broader. Now place the cork resting on the pins as legs and give it a slight tilt. Watch what happens. You will notice that in the first case, the cork topples down while in the second case, the cork comes back to the original position.

6) A uniform meter rod of weight 100 N carries a weight of 40 N and 60 N suspended from 20 cm and 90 cm mark respectively. Where will you provide a knife edge to balance the meter scale ?

If we assume the fulcrum to be at 50 cm mark, then the moment due to the force at 90 cm mark is greater than the one at 20 cm mark. Therefore, the knife edge should be supported at a distance of 'X' cm away from 50 cm mark.

40(30 + X) + 100 + X = 60 (40 - X)
120 + 4X + 10X = 240 - 6X (dividing by 10)
14X + 6X = 240 - 120
20X = 120, x=120/20 =6
The knife edge should be provided at 56 cm mark.

7) A see-saw of 4m is provided with a wedge at the center. Susan and Jason of weights 500 N and 300 N respectively are sitting on the same side of the fulcrum at 2 m and 1.5 m from center respectively. If Karl weighing 600 N is sitting on the opposite side at a distance of 2 m from the center where must Peter weighing 200 N sit to balance the see-saw?

Let Peter be at a distance of 'd' m away from center nearer to Karl as the moment on the opposite side is greater.

By the principle of moments,

(600 x 2) + (200 x d) = (500 x 2) + (300 x 1.5)

12 + 2d = 10 + 4.5 (dividing both sides by 100)

2d = 14.5 - 12

d= 2.5/2= 1.25cm

From the center near Karl.

8) Two ropes are attached to points P and Q on a wheel of radius 0.5 m which can turn about O. Equal forces of 10 N are applied on the ropes at P and Q. State whether the wheel will turn, if at all whether clockwise or anticlockwise. Support your answer with a scientific reason.

Moment due to force at P

= 10 x 0.5 = 5 N m (clockwise)

Moment due to force at Q.

= 10 x 0.4 = 4 N m (anticlockwise)

The force P is tangential perpendicular distance from O = 0.5 m while the perpendicular distance OR from Q = 0.4 m. Hence, the clockwise moment being greater the wheel will turn in that direction.

When a ship floats in the water the forces of buoyancy and gravity balance each other because they are equal.
The following three diagrams show how loads affect the center of gravity and stability of a ship. A fully loaded ship [figure (a)] brings the center of gravity and the center of buoyant force close together making the ship stable.

When the ship is unloaded [figure (b) above] the center of the gravity and the center of buoyancy have moved far apart, then the ship will be unstable.

10) Experiment to define the Centre of gravity ?

In a rigid body the particles are held together in affixed position relative to one another. Each particle is attracted towards the centre of the earth with a force equal to its weight. Let F1, F2, F3, F4, F5 be the forces acting on the particles P, Q, R, S, T, U respectively, and then the resultant force is equal to their Vector sum given by
F= F1 + F2+ F3 + F4+ F5
The line showing the direction of this resultant force is called the line of action. This total force or weight of the body appears to act through affixed point (G) irrespective of the position or orientation of the body. This point (G) is called the centre of gravity.

11) Explain the relation between the stability of a body at rest and position of centre of gravity ?

Consider a thin wooden ruler (a) and a thick cylinder (b) in the position. Give a push to both of them by applying equal force at their top ends. The thin ruler falls down easily. The thick Cylinder tilts aside slightly and regains its original position.therefore; the thick cylinder is more stable than that of the ruler. The base area of thick cylinder is more stable than that of the ruler. Then a body is more stable whenever its base area is larger.

12) How stability is utilized in constructing a ship ?

The principles of stability are utilized in constructing a ship. The base of the ship is made as large as possible and the height of the centre of gravity is made as small as possible so that the stability of the ship is very high.Inthe time of cyclone the wind blows with high speed and tides are produced with large energy. Due to wind and tides the ship tilts a side but it regains its original position so that it is in stable equilibrium.

13) Why a person walking on a rope carries along stick in his hands ?

A person walking on a rope holds a long pole in his hand. He changes the orientation of the pole such that the line of action of the total weight always passes through the rope so that he does not fall down.

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