FORCE OF GRAVITY, SOLIDS & FLUIDS
FORCE PF GRAVITY
Earth attracts everybody towards itself with a force known as ‘gravity’. Due to the force of gravity the ball thrown upwards doesn’t go upwards but it falls downwards after covering some vertical distance. Actually, every object attracts every other object towards itself with a force. This force is called the gravitational force. Gravitational force is one among the four fundamental forces. It is always attractive in nature.
NEWTON'S UNIVERSAL LAW OF GRAVITATION
Newton came to the conclusion that any two objects in the Universe exert gravitational attraction on each other.
Any two particles of matter anywhere in the universe attract each oilier with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them,
i.e., \[F\propto \frac{{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\] or \[F=\frac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\]
Here, the constant of proportionality G is known as the universal gravitational constant. It is termed a “universal constant” because it is thought to be the same at all places and all times.
\[G=6.673\times {{10}^{-11}}N{{m}^{2}}/k{{g}^{2}}.\]
Handy Facts
The value of universal gravitational constant, G is very small hence gravitational force is very small, unless one (or both) of the masses is huge.
Important Characteristics of Gravitational Force
- Gravitational forces are always attractive and always acts along the line joining the two masses.
- Gravitational force is a mutual force hence it is action-reaction force, i.e., \[{{\vec{F}}_{12}}=-{{\vec{F}}_{21}}\].
- Value of G is small, therefore, gravitational force is weaker than electrostatic and nuclear forces.
- Gravitational force is a central force because \[F\propto \frac{1}{{{r}^{2}}}\]
- The gravitational force between two masses is independent of the presence of other objects and medium between the two masses.
Importance of the Universal Law of Gravitation
The universal law of gravitation successfully explained several
- the force that binds us to the earth
- the motion of the moon around the earth
- the motion of planets around the Sun and
- the tides due to the moon and the Sun.
MASS AND WEIGHT
The quantity of matter in a body is known as the mass of the body. Mass is quantitative measure of inertia. Mass is an intrinsic property of matter and does not change as an object is moved from one location to another.
Weight, in contrast, is the gravitational force that the earth exerts on the object and can vary, depending on how far the object is above the earth’s surface or whether it is located near another body such as the moon.
The relation between weight W and mass m
\[E=\frac{G{{M}_{E}}m}{{{r}^{2}}};\,\,\,\,\,\,\,\,\,\,\,\,\,W=mg\]
As \[{{g}_{moon}}=\frac{1}{6}{{g}_{earth}}\] therefore,
\[{{w}_{moon}}=\frac{1}{6}{{w}_{earth}}\]
Inertial and Gravitational Mass
The mass
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