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2006-08-17 04:42:47 · 15 answers · asked by Anonymous in Science & Mathematics Physics

consider a cylinder(radius R & height h) and sphere(radius r) of equal volume V
now (4 pi r^3)/3=V
surface area=4 pi r^2=[ 36 pi V^2]^1/3
IN CASE OF CYLINDER
V=pi r^2 h
surface area= 2 pi r h=2v/r
comparing the surface areas
2V/r= [6 pi V^2]^1/3
hence s.a depends upon value of r chosen since V is constant.

2006-08-17 06:00:27 · update #1

15 answers

BECAUZ EVERY PARTICLE HAS MIMIMUM ENERGY UNDER EQUILIBRIUM...N IN A SPHERE ONLY IT IS POSSIBLE FOR ALL THE PARTICLES IN SUMMATION TO HAVE THE LEAST POTENTIAL ENERGY

2006-08-17 07:24:49 · answer #1 · answered by Anonymous · 1 0

The answer is in the Second Law of Thermodynamics, which says that net entropy is ever increasing. As Wikipedia puts it:

"The reason is twofold: first, maximizing entropy, in a sense, means minimizing the amount of prior information built into the distribution; second, many physical systems tend to move towards maximal entropy configurations over time." [See source.]

The offshoot of the SLT is that as physical things (mass) accumulate (like water molecules in a drop of rain) they tend to accumulate in a shape of least useful energy or, similarly, the most useless energy (entropy). The sphere happens to be that shape. Mother nature is lazy, why use more energy (useful energy) than is necessary to hold things together?

While gravity certainly plays a part in the shaping of large mass (like planets and stars), it plays little part in the small stuff (like rain drops). Surface tension, combined with the least useful energy driver, causes the raindrops to be spherical when they can (a falling raindrop gets bent out of shape by drag forces as it falls through the atmosphere to the ground).

At the subatomic level, other forces (and the old SLT minimum useful energy bit) come into play. Strong and weak forces, for example, are the binding energies in atoms.

At this level, specifying things as spherical becomes a bit more problematical. Because of effects at the subatomic level that we don't see in our observable world, neutrons, protons, and electrons are not so much spherical, but the space they might be found in is. Electrons are actually modeled as being located in a shell (a hollow sphere if you will) that surrounds the nucleous of an atom. In any case, these spherical spaces are also products of the entropy law.

If all this give you a headache...join the club.

2006-08-17 13:28:34 · answer #2 · answered by oldprof 7 · 0 0

Of all the shapes with a given volume, the one with the smallest surface area is the sphere. For water droplets, the surface tension acts to make that surface as small as possible, so you get spherical drops. Planets become spherical because they are large enough for gravity to pull them into a sphere (again, if everything is pulling together, the best shape is a sphere). Asteroids that are not large enough for gravity to be this effective will not be spherical. On the other hand, a rotating planet or star can be distorted awy from the spherical shape because of centrifugal forces from the rotation. Finally, the atoms are spherical because the electrons are trying to get as close to the nucleus as they are allowed to be. This again leads to a spherical shape. But once again, if there are other influences, like a magnetic field, this spherical shape can be distorted by them.

Now, about that spelling...... y iz it tat????

2006-08-17 12:53:18 · answer #3 · answered by mathematician 7 · 0 0

What makes you think they are spherical? Who knows what shape an electron is? It is too small to locate exactly much less picture. If we assume an atoms shape is defined by its valance electron clouds then its not a sphere. Some of the clouds are dumbbell shaped etc. Perhaps the answer to your question has something to do with the human brain. When we don't know what something looks like we tend to assume its a sphere or a circle. OR maybe we assume some things in nature are most basic because they are spherical? Is a planet really a basic thing in nature? It seems very complex to me.

2006-08-17 18:13:10 · answer #4 · answered by sparrowhawk 4 · 0 0

Its simple.. everything in nature tends to get stable and balanced. In all the shapes sphere has the least surface area for same amount of substance........
Now you might ask what does surface area has to do with stability??? actually all the particles of nature have some energy associated with them so they arrange themselves so as to attain the configuration which has the least energy. And spherical shape is the perfect answer.
Consider a simple analogy.... water always flows downwards not upwards....that's because it attains a state of lower energy at the bottom position. chemical reactions take place because the end product has lower energy than reactants hence more stable.
Being spherical or round also helps maintain a lower energy level so bassically everything tries to arrange itself in that shape.

noddy

2006-08-17 12:08:38 · answer #5 · answered by .:NoDdY:. 2 · 0 0

It looks that every thing in nature has a tendency to assume the shape of a sphere .Ther must certianlyy be a reason for it . Whetehr a substance other than a solid is in space or under the influence of the amospher of gasses , the nature of things is to assume the shape of a spher. The plausible reason seems to be that only in the case of the shape of sphere all the points on the surface on all sides of a quantity of substance is equidistant and this helps to maintain stability in its positon in equilibrium. In every other shape this position of equilibrium is not attainable .
so also all masses irrespective of their quantity should have a force of attraction . since any quantity of anymater is compsed of molecules of elements / compounds which in turn are composed of atoms of elements , they must be attracted to ward the center of the the mass of a ny quantity and this must also ensure an even distribution of the atoms / molecules of the mass on all sides equally again contributing to stability . The forces of atraction of of the atoms and molecules need not necessarily be at great and pronounced as that of a magnet . If the grea mass of the planets have their force of gravity , the small parts of it should also have that force in them in due proportion. Apart from this there seems to be no special magic in this phenomenon.

2006-08-17 12:10:51 · answer #6 · answered by Infinity 7 · 0 0

Use proper grammar or we won't know what you are talking about. Spherical because, if you believe in nature, everything will come back one point or another, sphere for life and death continuous. Otherwise because it is much more convenient than a cube or loose shape, more orderly that way.

2006-08-17 11:50:04 · answer #7 · answered by t_nguyen62791 3 · 0 0

Scientifically its proved that gravity & other forces acting on an object will compell the form to take a spherical shape.

So are the chromosomes in our body, our blood cells, and the shapeof lips when we utter the infathomable AUM.

Life originated from "O" and will end in "O"

2006-08-17 12:02:36 · answer #8 · answered by stoneman 3 · 0 0

because of the equal attractive forces. for planets its de gravity and for water droplets its the inter molecular forces. in the absence of a net force, molecules attract each other and since the attraction is equal on all sides. the result is a sphere, as it is rounded and equal on all sides. As for planets, de same apply except its gravity not inter molecular forces. As for electrons. well its not exactly round, its juz a charge

2006-08-17 12:36:44 · answer #9 · answered by ThoughTs 2 · 0 0

okay about all the above answers and the correct reason i think is

only shere have lesser surfac area for more volume

i think it is a VI or VII th std question

2006-08-17 12:07:56 · answer #10 · answered by raghu 2 · 0 0

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