Question

prove that centre of gravity of a body is unique.....pls answer it with full explanation

Answer 1

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Throw a ball in the air and gravity pulls it straight back down. Not everything moves like this when gravity acts on it. Most objects are not nice, neat shapes like balls. That means gravity acts on them in more complex ways. Even so, all objects behave as though theirmass (the stuff they're made from) is concentrated at a point called their center of gravity. A simple object like a ball has its center of gravity in a very obvious place: right at its center. But in a more complex object, like your body, the center of gravity is slightly higher than your waist because there's more weight in the top half of your body than in the bottom half.

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Force of gravity acts vertically downward.If the body is moved from one point to another horizontally then the force of gravity is not causing the motion. So, the work done by the force of gravity is zero.

W = Fs cosθ

= Fs cos 90°

= 0

Gravitational potential energy (U) is the amount of work done against gravity to take a body away from the earth’s surface (where h = 0).

U = -GMem/r

Me = mass of earth, m = mass of object, r = distance between the center of earth and the object.

The gravitational potential energy of an object at infinite distance from the earth is zero. So, the work done in moving the object from earth to infinity increases the potential energy of the object from a negative value to zero (zero is greater than negative).

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Answer 2

Centre of gravity, in physics, an imaginary point in a body of matter where, for convenience in certain calculations, the total weight of the body may be thought to be concentrated. The concept is sometimes useful in designing static structures (e.g., buildings and bridges) or in predicting the behaviour of a moving body when it is acted on by gravity.
In a uniform gravitational field the centre of gravity is identical to the centre of mass, a term preferred by physicists. The two do not always coincide, however. For example, the Moon’s centre of mass is very close to its geometric centre (it is not exact because the Moon is not a perfect uniform sphere), but its centre of gravity is slightly displaced toward Earth because of the stronger gravitational force on the Moon’s near side.
The location of a body’s centre of gravity may coincide with the geometric centre of the body, especially in a symmetrically shaped object composed of homogeneousmaterial. An asymmetrical object composed of a variety of materials with different masses, however, is likely to have a centre of gravity located at some distance from its geometric centre. In some cases, such as hollow bodies or irregularly shaped objects, the centre of gravity (or centre of mass) may occur in space at a point external to the physical material—e.g., in the centre of a tennis ball or between the legs of a chair.

The centre of gravity of any body can also be determined by a simple physical procedure. For example, for the plate in the figure, the point G can be located by suspending the plate by a cord attached at point A and then by a cord attached at C. When the plate is suspended from A, the line AD is vertical; when it is suspended from C, the line CE is vertical. The centre of gravity is at the intersection of AD and CE. When an object is suspended from any single point, its centre of gravity lies directly beneath that point