FORCE

It is defined as a push or pull that changes or tends to change the state of rest or of uniform motion of
a body along a straight line.

Newton’s Universal law of gravitation
“Everybody in this universe attracts every another body with a force which is (i) directly
proportional to the product of their masses and (ii) inversely proportional to the square of the
distance between their centers”.

Consider a body of mass m 1 attracts another body of mass m 2 with a force F towards its centre O 1 .
The body of mass m 2 in turn attracts the body of mass m 1 with the same force F towards its centre
O 2 . Suppose the distance between their centers is‘d’ then, according to Newton’s universal law of
gravitation, we have

F∞m 1 .m 2 ………….(i)

And F∞1/d^2.………..(ii)
Combining these two equations (I) and (ii), we have

F∞Fm1m2/d^2

Or, F = GFm1m2/d^2 ………….(iii)
Where G is called a proportionally constant or universal gravitational constant. The value of The
G is determined form experiment.

Hence, the equation (iii) gives the measure of the gravitational force between two masses.
Universal gravitational constant ‘G’
Universal gravitational constant ‘G’ can be defined as the force of gravitation that is exerted between
two unit masses, separated from one another by a unit distance.
The SI unit of G is Nm 2/ kg -2 .
The approximate value of G is 6.6710 -11 Nm 2/kg -2 .

Properties of G
i. The value of G is independent of the nature and chemical composition of the masses of the
bodies, and the medium in which the bodies are occurred.
ii. The value of G is unaffected by temperature and pressure.

Consequences of gravitational force
i. The presence of solar system and planets revolve round the sun due to the presence of
gravitational force.
ii. The presence of atmosphere on the earth is due to the gravitational force.
iii. The gravitational force of the earth keeps us firmly on the surface of the earth.
iv. Tides in seas and oceans are due to the gravitational force of the sun and moon.

Special features of gravitational force
i. The gravitational forces between two bodies constitute on action and reaction pair.
ii. The gravitational force between two bodies does not depend upon the nature of the
intervening medium.
iii. The gravitational force between light bodies is extremely small and hence such smaller
force is not felt in practice. However, it becomes appreciable in case of massive bodies.

Gravity or weight
The force of attraction of the earth on a body is called force of gravity or simply the weight of the
body on earth.
Let a body of mass m be placed on the surface of the earth of mass M as shown in the figure. The
distance between them can be taken to be equal to the radius (R) of the earth. The weight (W) of the
body on the surface of the earth is given by,

W = GMm/R^2 …………….. (i) (
If m is kept constant,

W∞M/R^2 ……….. (ii)
Equation (ii) shows that weight (W) of a body on the surface of a planet/ satellite is directly
proportional to mass (M) of the planet /satellite. Greater the mass of the planet /satellite, larger its
gravity is i.e., greater will be the weight of the body on the planet/satellite.
Equation (ii) also shows that weight (W) of a body on the surface of a planet/satellite is inversely
proportional to the square of the radius (R) of the planet/satellite. The weight of the body will be less
if it becomes large.

Effects of gravity
1. We are able to stand up, run and perform other activities freely due to gravity of the earth.
2. Construction of building and bridges is possible due to the gravity of the earth.
3. There will be no atmosphere around the earth in the absence of gravity of the earth.
4. If a body is thrown upwards, its notion is opposed by gravity of the earth. So, it falls back
to the earth.
5. Tides occur by the gravity of the moon on ocean water.