SEE SCIENCE : FORCE

Force:
Force is defined as a push or pulls that change
or tends to the state of the body whether it is at
rest or in uniformmotion along the straight line.
Force is a vector quantity.

Newton law of gravitational: Newton’s Law of
Gravitation states that “The force of attraction
between the two bodies is directly proportional
to the product of their masses and inversely
proportional to the square of the distance
between their centers.”
Why Newton’s law of gravitation
is called universe law?
Newton’s law of the
gravitation holds true or applicable for all the
objects present in this universe whether the
objects be terrestrial or celestial. The
gravitational force exists everywhere in this
universe. Therefore Newton’s law of gravitation
is called universe law.

Verification of Newton’s law:
Consider the two bodies of the mass m₁ and
m₂ with force F acting between them towards
their centre. If the distance between their
centers is d then,

According to Newton’s universal law of
gravitation,
We have F ∝ m₁m₂ ……1
F ∝ 1/d²
Combining I and 2 we get F  ∝ m₁m₂ /d²
F=Gm₁m₂ /d²
Where G is proportionality constant which is
known as universal gravitational constant.
The numerical value of gravitational constant
(G) is 6.67×10⁻¹¹ and its unit is Nm²/Kg²

Properties of G:
Value of G is independent of the temperature,
pressure, nature of the intervening medium and
chemical composition of the masses of the
bodies.
Gravity:
It is the force which pulls an object towards the
centre of the earth.
Acceleration due to gravity : The acceleration
produced in a freely falling body due to the
influence of gravity is called Acceleration due to
gravity.
Its symbol is “g” and its SI unit is meter per
second (m/s ).
Relation between acceleration due to gravity
and radius of the earth
Let M be the mass and R be the radius of the
earth and m be the mass of the body kept at the
surface of the earth.

According to the Newton’s law of gravitation
the force of attraction between them is given by
F=G Mm/R² ………………………1
Also the body is attracted towards the centre of
the earth with a force given by
F=mg…………………..2
From 1 and 2, mg = G Mm /R
g=GM/R² …………….3
G and M are constant whereas R varies because
radius of the earth is more at the equator than
at poles.
From 3,
We can say that the acceleration due to the
gravity is independent to the mass of the body
but depends on the mass and radius of the
earth.
Variation of the value of g:
a. Variation due to the shape of the earth:
     g∝ 1/R²
Value of the g maximum at poles but
minimum at equator
b.Variation due to the height from the surface
of the earth: g’ = (R/R+h)² g
If we increase the height from the surface of
the earth the quantity in the bracket becomes
less than 1.
And the acceleration due to the gravity
decreases as height from the surface is
increased.
c. Variation from the depth of earth surface:
g’ = GMₐ/a².
where Mₐ is mass of earth with in radius a.
    =Gρ(4/3 πa³)/a² (ρ density of earth)
    =⁴/₃Gρπa
∴ g'∝a
as a tends to zero, g' also tends to zero.

Gravitational field and Gravitational field
intensity:
The space around the mass where gravitational
force of influence of the mass can be felt is
called gravitational field.
Gravitational field intensity is the force
experienced by the unit mass kept at that point.
It is given by
Gravitational Field intensity (I) = Force
experienced / mass
If the body of mass m is kept at the distance d
from the centre of the earth of mass M and
radius R
Figure:(below)
Then force experienced by the mass is given by
F = G Mm/d²
To calculate the gravitational field intensity we
have to take a unit mass so m =1
Gravitational field intensity (I) = GM/d²
If the body is at the surface of the earth d = R
(I) = G M/R²
This is numerically equal to the acceleration
due to gravity.

Mass: It is the quantity of matter contained in
the body. It is scalar quantity.

Weight: It is the force with which the object is
attracted towards the centre of the earth. It is
vector quantity.

Weight=mass * gravity.
Weight depends upon
gravity and gravity depends on the distance.
E.g. As the stone is away from the earth surface
the weight of the stone is less than the stone
present in the bottom.

Free fall: When an object is falling towards the
surface of the earth only under the influence of
gravity without external resistance, the fall of
the object is free fall.

Weightlessness: Weightlessness is the condition at which the apparent weight of a body is zero. Weightlessness is possible in the absence of gravity.

Questions For practise from Force

# Important Questions for SLC Examination

1) Define gravitation.

Why the moon does not moves farther from

earth although it is moving round the earth ?

2).Which force doesn’t let the earth go outside its

orbit ?

3).State reason; large mass of water go up when

the moon or the sun comes over the sea.

Larger tide is produced when the moon comes

over the sea than the sun do so. What does it

justify ?

4).State law of gravitation.

5).What relation is there in between gravitation

and distance between two masses ?

6).What types of relation is there between

gravitation and magnitude of masses ?

7).What is change in gravitational force in between

two bodies if

a.Mass of one of them is halved ?

b.The mass of both of them is doubled ?

c.The distance between them is doubled ?

8)  Derive F =GM₁m₂/R²

9) What is G ? Why is it called universal ?

What is unit of G ? Justify it.

10) How much gravitational force is produced

between two masses 1 kg each are kept at a

distance of 1 meter ?

11) Define gravity.

What change in gravitational force if the earth is

pushed towards the sun ?

12) Why don't we feel gravitation between two

bodies separated by some distance ?

13) Define weight of a body.

Mass of mountain is 3x10¹⁰ kg. A man with

mass of 100 kg is standing 100m from the centre

of the mountain. Find gravitational force

between the man and mountain.

Find amount of mass that should be kept at

distance of one metre from one kg of mass to

exert 1 Newton of gravitational force.

14) What will be weight of 5 kg of rock on the

surface of Jupiter ? Mass and radius of Jupiter

are 1.9 x 1027 kg and 7.1 x 107 m respectively.

15) Define

a)Gravitational field

b)Intensity of gravitational field

16) Derive the formula to calculate intensity of

gravitation. What does the intensity of

gravitation depend on ? Find the unit of

intensity of gravitational field ?

17) If the intensity of gravitational field is x unit at

the surface of earth. What will be its value at

the point at the height that equals to length of

radius of the earth ?

18) Intensity of gravitational field is 9.8 N/kg. If the

earth contracts till its radius becomes where R

is radius of earth at present, what will be new

value of intensity of gravitation ?

19) Mass and radius of earth are M and R. And mass

and radius of Jupiter are 318x and 11y. How

many times is the gravitational field intensity of

Jupiter as compared to that of the earth ?

Where will the weight of unit mass be more out

of bottom and tip of a mountain ? Given reasons

to justify your answer.

20) List the effect of gravity with 4 examples of

each, which are favorable and unfavorable to

our daily activities.

21) Define the term acceleration due to gravity.

What is the gravity effect of ? Explain.

Are accelerations due to gravity of small stone

and big stone

equal ? Give reasons.

22) There is gravitation at force between an apple

hanging from a tree and the earth. Why doesn't

the earth go toward the apple ?

23) What does the Newton’s experiment on a stone

and feather prove ?

Do a stone and feather fall at equal rate if both

are let to fall at once ? What will be result of

such experiment if it is held in moon ? Explain

with reasons.

24) Derive  g =GM/R²

State relations of g with mass and radius of a

massive body separately.

What is meant by g = 9.8 m/s² ?

Why is value of g less at top of mountain than at

its bottom ?

Why is value of g less in moon than in earth ?

25) Distinguish between g and G.

Prove : g =GM/R²

What does the acceleration due to gravity

depend on ?

26) Find the mass that could be lifted in moon, by a

person who can lift 2000N of weight in the earth.

Why is it easier to lunch a rocket in moon than

to do so in the

earth ?

27) Differentiate between g and E, E= Intensity of

gravitational field.

28) Define the term free fall.

What is the difference between falling of stone

and paratrooper from a plane ?

29) A paratrooper lands safely in the earth although

he jumps from very high land will he safely if he

falls from very height on the moon ? Give

reasons.

30) Why does water not come down through the

hole at the bottom of cup while the cup filled

with water is falling freely ?

31) Why does a person feel no notion to trade

elevator while elevator falls freely ?

32) Define weightlessness.

State reason for a body is weightless while it is

falling freely.

33) State three conditions in which a body is

weightless.

34) Define null points.

Can water be poured from one vessel to another,

in null points ? Explain with reasons.

35) Distinguish the weightlessness of a body in a

space from the weightlessness in free fall of a

body.