Gravitation

Gravitation :-
The force between any two object in this universe due
to masses of the bodies is called gravitational force.
(Always attractive in nature).

Gravity :-
The force with which the earth pulls the object towards
it’s centre is called “the gravity of the earth.
 Universal law of gravitation
According to this law,
“The force of attraction between any two bodies in the universe is directly
proportional to the product of their masses and inversely proportional to the square
of distance between them.”

• It was given by Isaac Newton.

• It also known as Newton's law of gravitation.
Consider two bodies A and B having mass m1 and m2 & whose centre at a distance
d from each other.

m1 m2

• •
d

Then force between two bodies is directly proportional to the product of their
masses i.e.
F ∝ m1m2 ……………1
And the force between two bodies in inversely proportional to the square of the
distance between them i.e. 𝟏
F ∝ 𝟐 …………………2
𝒅
Combining both equation 1 and equation 2, we get

m1m2
F∝
𝒅𝟐

G m1m2
F=
𝒅𝟐

Here, G → Universal gravitational constant

G = 6.67 x 10-11 N – m2 / kg2
 Importance of universal law of gravitation
• The universal law of gravitation successfully explained several phenomena
given as below :-

▪ This law explain the cause of revolution of moon around earth and revolution of
planets around sun.
▪ The causes of tides due to the gravitational force of attraction moon and sun.
▪ It helps in construction of aircrafts, space shuttle rockets, artificial satellite etc.
Que. Find the gravitational force between earth and an object of 2kg mass placed
on its surface (given mass of the earth = 6.4 x1024 kg and radius of the
earth = 6.4 x106m)
Que. The mass of the mars is 6.39 x1023 kg and that of the Jupiter is 1.89 x1027 kg.
If the distance between mars and Jupiter is 7.49 x105 m. calculate the
force exerted by the Jupiter on the mars. (G = 6.7 x10-11nm2/kg2)
 Acceleration due to gravity (g)

• The acceleration produced in a body due to earth’s gravitational force is called

as gravitational acceleration.
• It is denoted by “g”
• S.I. unit of g is the same as that of acceleration i.e. m/s2.
 Let,
Mass of the earth be “M” and an object falling freely towards it be “M”. The
distance between centers of the earth and the object is R.

From Newton's law of gravitation,

𝐺𝑀𝑚
F= ………….l
𝑅2
Also, from second law of motion, force exerted on an object
F = ma
since a = g (i.e acceleration due to gravity)
F = mg ……………2
from eqn l & eqn 2
𝐺𝑀𝑚
mg =
𝑅2
 𝐺𝑀𝑚
g=
𝑅2
From the formula, it is clear that acceleration due to gravity does not depend on
the mass of a falling object.
If depends only on the mass of the earth or celestial bodies.
We can calculation the value of g
mass of earth M = 6 x1024 kg
radius of earth R = 6.4 x106 m
Universal gravitational constant G = 6.67 x10-11 N-m2/kg2
So,
𝐺𝑀𝑚
g=
𝑅2
6.67 x10−11 N−m2/kg2 x 6 x1024 kg 𝑚
g= g = 9.8 m / s2
6.4 x106 m
 Equations of motion for free fall
In case of motion of bodies under free fall, there is a uniform acceleration, i.e.
acceleration due to gravity (g) acting downward.

General equation of Equation for body under free fall

motion
V = u + at V = u + gt [∵ a = g]
S = ut + ½ at2 S = ut + ½ gt2 [∵ a = g]
V2 = u2 + 2as V2 = u2 + 2gh [∵ a = g]

Where, h= height from which the object falls.

t= time of fell, u= initial velocity, v= find velocity,
g= acceleration.
Que. Mass of the moon is Mmoon = 7 x1022 kg and it’s radius is Rmoon =
1700km. using the equation find the value of acceleration on the surface of
moon for an object of mass “m”.
➢ what will be gravitational force between two objects.

If 1. The mass of one object is doubled.

2. The distance between the object is tripled.
3. Mass of bath the object is doubled.
Que. A care falls off a ledge and drops to the grounds in 0.6s.
The value of g is 10 m/s2.
Find:- 1) what is its speed on striking the ground ?
2) what is its average speed during the 0.6s ?
3) how high is the ledge from the ground ?
Que. An object is thrown vertically upwards and rises too a height of 13.07m.
Calculate:- 1) the velocity with object was thrown upwards
2) the time taken by the object to reach highest point.
Que. A ball is thrown vertically upwards with a velocity of 25 m/s. if g 10 m/s2
then calculate
1. Height it reaches.
2. Time taken to return back.
Que. A ball is thrown vertically upwards with a speed of 49 m/s. calculate.
1) Maximum height of the ball. (120.5m)
2) Total time taken by the ball to reach the earth surface. (9.8sec)
Que. The force of gravitation between two bodies is F. In what situation will be
the force between the two bodies become 4F.
Mass :- (m)
• Mass is the quantity of matter contained in a body.
• It is a scalar quantity.
• S.I. unit of mass is kg (kilogram).
• Mass always remains constant everywhere. The mass of the body cannot be
zero.

Note:- The centre of mass of a body may be defined as the point at which whole
mass of the body may be assumed or concentrated.
Weight :- “W”
❖ Weight of an object is the force by which an object is attracted towards the
earth.
F = ma
F=mxg

Force of attraction of the earth on an object is known as the weight of the object
Weight of an object w = mg.
• It is a vector quantity.
• S.I. unit is Newton (N).
• Weight of an object is not constant, it depends upon the place.
• In the space, where g = 0, weight of an object is zero.

Note:- the weight of an object on the moon is one-sixth of its weight on the earth.
1
Wm= We
6
Que. Mass of object is 12kg. calculate:-
1) It’s weight on the earth.
2) It’s weight on the moon.
Que. A man weighs 600N on the earth, what is his mass. If g is 10m/s2 ? On the
moon, his weigh would be 100N. What is the acceleration due to gravity
on the moon ?
Que. If the moon attracts the earth, they why does the earth not move towards the
moon ?

Ans. The earth and the moon experience the gravitational force from each other.
However, the mass of the earth is much larges than the mass of the moon. Hence, if
acceleration towards the moon is much smaller than the acceleration of the moon
towards the earth. That’s reason for the earth does not move towards the moon.
 Thrust

• Thrust is the force acting on an object perpendicular to its surface.

• Effect of thrust depends on the area on which it acts.
• S.I. unit of thrust is Newton (N)
• It is a vector quantity.

F
F F
 Pressure

Pressure is the force acting perpendicularly on a unit area of an object.

𝐹𝑜𝑟𝑐𝑒 (𝐹) 𝑇ℎ𝑟𝑢𝑠𝑡
Pressure (P) = =
𝐴𝑟𝑒𝑎 (𝐴) 𝐴𝑟𝑒𝑎

• S.I. unit of pressure is N/m2, which is also called Pascal (Pa).

• It is a scalar quantity.
• A force acting on a smaller area exerts a large pressure while the same. Force
acting on a larges area exerts a small pressure.
Que. Force of 200N is applied to an object of area 4m2. find the pressure.
Que. A block wood is kept on a table top. The mass of wooden block is 6kg and
its dimensions are 50cm x 30cm x 20cm.
Find the pressure exerted by the wooden block on the table top, if it is made to lie
on the table top with it’s side of dimensions.
1) 30cm x 20cm
2) 50cm x 30cm
 Some daily life application of pressure
• The handles of bags, suitcases etc are made broad, so, that less pressure is
exerted on the hand.
• Buildings are provided with broad foundations, so that the pressure exerted on
the ground becomes less.
• Railway tracks are laid on cement or iron sleepers. So that the pressure exerted
by train could spread over the large area and thus pressure decreases.
• Pins, needles and nails are provided with sharp pointed ends to reduce the area
and hence, to increase the pressure.
• Cutting tools have share edges to reduce the area, so that lesser force, more
pressure could be exerted.
• Pressure on ground is more when a man is walking than. When he is standing
because in case of walking, the effective area is less.
 Pressure in fluids

All liquids and gases are together called fluids, water and air two most common
fluids.
 Buoyancy:-

• The tendency of a liquid to exert an upward force on an object immersed in it is

called buoyancy.
• Buoyant force is an upward force which acts on an object when it is immersed in
liquid. It is called up thrust.
 Floating as sinking of object in liquid :-
When an object is immersed in a liquid, then following two force at on it.

• Weight of the object which acts in downward direction. i.e.

It tends to pull down the object.
• Buoyant force (up thrust) which acts in upward
direction i.e.
It tends to push up the object.
• There are three conditions of floating and sinking of
objects as given below.
Therefore are three condition of floating and sinking of object as given below;

1. If the buoyant force (up thrust) is less than the weight of the object. The object
will sink in the liquid.
2. If the buoyant force is equal to the weight of the object. The object will float
in the liquid.
3. If the buoyant force is more than the weight of the object. The object will rise
in the liquid.
Sink Float Rise
 Archimedes's principle

It states that “when an object is fully or partially immersed in a liquid, it

experiences a buoyant force or thrust, which is equal to the weight of liquid
displaced by the object.
i.e.
Buoyant force or upthrust acting on an object
= weight of liquid displaced by the object
F(bouyant) = W(displaced liquid)
 Application of Archimedes's principle

Archimedes’ principle is used in

▪ Designing ships and submarines
▪ Manufacturing of boat.
▪ Lactometer (a device used to determine the purity of milk)
▪ Hydrometer (a device used for determining the density of liquid).
NCERT Questions :-
Que. Gravitational force on the surface of the moon is only 1/6th as strong as
gravitational force on the earth. What is the weight in Newton of a 10 kg
object on the moon and on the earth.
Que. A stone is released from the top the of a tower of height 19.6m. Calculate its
final velocity just before touching the ground.
Que. A stone is thrown vertically upward with an initial velocity of 40m/s. taking
g =10m/s2, find the maximum height reached by the stone. What is the
net displacement and the total distance covered by the stone ?
Que. Calculate the force of gravitation between the earth and the sun. given that
the mass of the earth = 6 x1024 kg and of the sun = 2 x1030 kg. the average
distance between the two is 1.5 x1011 m.
Que. A ball thrown up vertically returns to the thrower after 6s. Find :-
1) The velocity with which it was thrown up.
2) The maximum height it reaches.
3) And it’s position after 4s.
Que. A sealed can of mass 700g has a volume of 500 cm3, will this can sink in
water? (Density of water is 1 gcm-3)
Que. The volume of 50g of a substance is 20 cm3 if the density of water is 1 gcm-3
will the substance float or sink?
Que. The volume of a 500 g sealed packet is 350cm3 will the packet float or sink
in water, if the density of water is 1 gcm-3 ? What will be the mass of the
water displaced by this packet ?