Science Class IX Abhyasa classes

Gravitation
1. Gravitation
2. The Universal Law of Gravitation
3. Free Fall
4. The Value of g
5. Mass and Weight
6. Weight of an Object on the Moon
7. Thrust and Pressure
8. Buoyancy
9. Archimedes’ Principle

 Gravitation
 In 1666, Newton saw an apple fall and wondered, "Why did it
fall straight down?"
He realized a force must pull objects toward Earth, the same
force that keeps planets in orbit. He named this force gravity,
leading to one of the greatest scientific discoveries.

 Centripetal force:
 A stone tied to a thread moves in a circle due to centripetal
force, acting towards the centre.
 Example: Earth's gravity provides the centripetal force for the
Moon's orbit.
 Circular motion involves constant direction change, altering
velocity.
 Centripetal force ensures circular motion, preventing the
object from moving straight.
 The Moon's orbit is maintained by Earth's centripetal force.
 Definition: A force that acts on a body moving in a circular
path and directed towards the center around which the body
is moving is called Centripetal force.

 Gravitation:

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Science Class IX Abhyasa classes

 “Gravitation or just gravity is the force of attraction

between any two bodies.”
 Gravitation Examples:
o The force that causes the ball to come down is known
as gravity.
o Gravity keeps the planets in orbit around the sun.
o Gravity is the force that causes a rock to roll downhill.

 Newton’s law of gravitation:

 Newton’s Law of gravitation states that every object in the
universe attracts every other object by a force that is
directly proportional to the product of their masses and
inversely proportional to the square of the distance
between them.
 Let there are two objects of mass m1 and mass m2 and the
distance between the objects is r, then according to law of
universal attraction, the attraction between the objects
F ∞ m1 . m2
1
F∞ 2
r
Therefore,
m1 . m2
F∞ 2
r

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Science Class IX Abhyasa classes

m1 . m2
Or F = G 2 , where G is constant whose value is 6.67 ×
r
−11
10 .
Questions:
1. Derive unit for gravitational constant (G):

2. The Earth is acted upon by the gravitational force of the sun, even
though it does not fall into the Sun. Why?

3. A stone and the Earth attract each other with an equal and opposite
force. Why then do we see only the stone falling towards the Earth
but not the Earth rising towards the stone?

4. How does the force of gravitation between two objects change when
the distance between them is reduced to half?

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Science Class IX Abhyasa classes

5. Determine the gravitational force if the masses of two bodies are 80

kg and 200 kg and they are separated by distance of 6 m.

6. What is the magnitude of the gravitational force between the Earth

and a 1 kg object on its surface? (Mass of the Earth is 6 x 10 kg and
radius of the Earth is 6.4 x 10 m.)

 Importance of the universal law of gravitation:

 The force that binds us to the earth.
 The motion of moon around the earth.
 The motion of earth around the sun.
 The tides due to moon in the sea.

 Acceleration due to gravity (g).

 According to Newton’s law of gravitation:
G= gravitational constant
M= mass of Earth
m= mass of object
R= Earth’s radius

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Science Class IX Abhyasa classes

M .m
We know, F = G 2
R
Also, F = m × g
M .m
So, m × g = G 2
R
G× M
Therefore, g = 2
R
 Values on Earth,
G= 6.673 × 10−11 Nm2/ Kg2
M = 6 × 1024 kg
R = 6.37 × 106 m
 By substituting the value, we get
g = 9.86 m/ s2

 Variation in value of g.
 Altitude
o g decreases as you move away from the Earth's surface
because the Earth's radius increases.
 Depth
o g decreases as you move deeper into the Earth because
the Earth's mass decreases faster than its radius.
 Latitude
o g is highest at the poles and lowest at the equator
because the Earth is not a perfect sphere. The Earth
bulges at the equator and flattens at the poles, so the
radius is larger at the equator.

Questions:

1. Why does a body reach the ground quicker at the poles than at
the equator when dropped from the same height?

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Science Class IX Abhyasa classes

2. (i) What will be the effect on the value of g when we go up a hill?

(ii) Calculate the value of g at the surface of the Earth.

3. A planet whose mass and radius are both half of that of earth.
Acceleration due to gravity(g) at its surface should be:

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Science Class IX Abhyasa classes

 Difference between G and g.

G g
Universal gravitational constant Acceleration due to gravity
It is constant everywhere in the It varies from planet to planet
universe
G= 6.673 × 10−11 G = 9.8
Unit: Nm2/ Kg2 Unit: m/ s2

 Mass and Weight.

 Mass
 It can be defined as the measure of the amount of matter in a
body.
 The SI unit of mass is Kilogram (kg).
 The mass of a body does not change at any time.
 Weight
 It is the measure of the force of gravity acting on a body.
 W=m×g
 As weight is a force its SI unit is also the same as that of force,
SI unit of weight is Newton (N).
 It depends on mass and the acceleration due to gravity, the
mass may not change but the acceleration due to gravity does
change from place to place.
 The weight of an object on the Moon is 1/6 times the weight
on Earth.

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Science Class IX Abhyasa classes

Sr Mass Weight
no
1. Mass is a scalar quantity Weight is a vector quantity
2. Mass remains the same Weight changes from place to
everywhere. place and is zero at
the center of the Earth.
3. Mass is measured using a Weight is measured using a
traditional spring balance.
balance.
4. The unit of mass is kilogram The unit of weight is Newton (N)
(kg) or gram (g).
5. Mass can never be zero. Weight can be zero depending on
the
gravitational force acting on it.
6. Mass does not change based Weight changes based on
on location. location, depending on
gravity.

Questions:

1. Find the weight of an 80 kg man on the moon’s surface. Calculate

his mass on the earth and the moon?
(The weight of an object on the moon is approximately 1/6 of its
weight on Earth)

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Science Class IX Abhyasa classes

2. The weight of any person on the Moon is about 1\6 times that on the
Earth. He can lift a mass of 15 kg on the Earth. What will be the
maximum mass he can lift by applying the same force on the Moon?

 Free fall.
 When an object is thrown upward, it reaches certain height,
then it starts falling down towards earth. It is because the
earth‘s gravitational force exerts on it.
 This fall under the influence of earth is called ‘free fall of an
object’

Initial velocity, u= 0 m/s

Prof. Sarvesh N. Nakshane

Science Class IX Abhyasa classes

Sr no Motion Gravitation
1st equation v = u + at v = u + gt
2nd equation 1 2 1 2
h = ut + at h = ut + gt
2 2
3rd equation v = u + 2 as
2 2
v = u + 2 gh
2 2

Questions:

1. A stone is released from the top of a tower of 20 m. Calculate

its velocity just before touching the ground.

2. On the Earth, a stone is thrown from a height in a direction

parallel to the Earth's surface while another stone is
simultaneously dropped from the same height. Which stone
would reach the ground first and why?

3. A car falls off a ledge and drops to the ground in 0.5 s. Let
g=10 m/s, (for simplifying the calculations).
(i) What is its speed on striking the ground?
(ii) What is its average speed during the 0.5 s?
(iii) How high is the ledge from the ground?

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Science Class IX Abhyasa classes

4. A stone is dropped from a height of 10 m on an unknown

planet having g = 20 m/s. Calculate the speed of the stone
when it hits the surface of the planet. Also, calculate the time
it takes to fall through this height.

 Kepler’s Law
1. Kepler’s Law of Orbits: Planets move around the Sun in oval-
shaped paths called elliptical orbits, with the Sun located at one
of the two fixed points called foci.

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Science Class IX Abhyasa classes

2. Kepler’s Law of Areas: As a planet moves in its orbit, the

imaginary line between the planet and the Sun sweeps out equal
areas in equal time intervals. This means the planet moves faster
when it is closer to the Sun and slower when it is farther away.
3. Kepler’s Law of Periods: The time a planet takes to complete
one orbit around the Sun is related to its distance from the Sun.
Specifically, the square of the time (the orbital period) is
proportional to the cube of the average distance from the Sun.

 Thrust
 Force acting on an object perpendicular to the surface is
called thrust. The effect of thrust depends on the area of
contact.
 SI unit: Newton.

 Pressure
 It is defined as Thrust acting on per unit AREA.
 SI unit: Pascal (Pa) or N/m².
 Pressure = Thrust/Area

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Science Class IX Abhyasa classes

Questions:

1. Why does a sharp knife cuts better than a blunt knife?

 A sharp knife cuts better because it has a smaller edge area,
creating higher pressure when force is applied. This higher
pressure
makes it easier to cut through materials. A blunt knife, with a
larger
edge area, produces lower pressure, making cutting less
effective.

2. Why is it difficult to hold a school bag having a strap made of a thin

and strong string?
 Holding a school bag with a thin string strap is difficult
because the small surface area of the string concentrates the
weight of the bag onto a tiny area of your shoulder, creating a
high pressure point and making it uncomfortable to carry;
essentially, the smaller the surface area, the greater the
pressure exerted on that area.

3. Why do nails have sharp ends?

 A nail has a pointed end so that the surface area is less, when
the surface area is less the pressure increases which makes it
easy for the nail to be driven into the wall or where ever it
may be inserted.

4. Why does camel have broad feet?

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Science Class IX Abhyasa classes

 Camels' broad feet spread out over the sand, giving them a
larger surface area to distribute their weight. This reduces
pressure and prevents them from sinking.

 Pressure in fluids
 Pressure exerted by liquids is due to the weight of the liquid.
 Characteristics of Pressure exerted by Liquids:
o At a given depth, pressure remains the same.
o It depends on the height or depth of the liquid.
o It is independent of size and shape of the container.
 Buoyant force
 The buoyant force or Buoyancy is the upward force exerted on
an object wholly or partly immersed in a fluid. This upward
force is also called Upthrust. Due to the buoyant force, a body
submerged partially or fully in a fluid appears to lose its
weight, i.e. appears to be lighter.
 The following factors affect buoyant force:
o Density of the Fluid: A denser fluid (like saltwater) exerts
more buoyant force because it pushes harder against
objects submerged in it.
o Volume (Surface Area) of the Object: Larger objects
experience stronger buoyant force as they displace
more fluid, which increases the upward force acting on
them.

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Science Class IX Abhyasa classes

 Law of flotation.
1. A body will float in a liquid if its density is less than the density of
the liquid.
2. A body will be in equilibrium at any submerged depth if the
density of the body is equal to the density of the liquid.
3. A body will sink in a liquid if its density is greater than the density
of the liquid.
 Floating: Object floats if buoyant force = weight of the object.
 Sinking: Object sinks if buoyant force < weight of the object.
 Suspended: Object remains suspended if buoyant force ≈
weight and **density.

Question:

1. Why it’s easier to swim in sea water then fresh water?

 Sea water contains dissolved salts which makes its
density more than river water. Hence, upthrust is more
in sea water than river water So it is easier to swim in
sea water than in river water.
 Archimedes’ Principle
 “Archimedes' principle states that when an object is
partially or fully immersed in a fluid, it experiences an
upward force called the buoyant force that is equal to
the weight of the fluid displaced by the object”
 Application of Archimedes’ principle:
 Submarine: A submarine floats or sinks by changing the
amount of water in its tanks. More water makes it
heavier and it sinks because the buoyant force (weight
of displaced water) is less than its weight. Less water
makes it lighter, and it floats because the buoyant force
is greater than its weight.
 Hot-Air Balloon: A hot-air balloon rises when the air
inside is heated because it becomes lighter than the
surrounding air. This means the buoyant force (weight of

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Science Class IX Abhyasa classes

displaced air) is greater than the weight of the balloon.

When the air cools, the balloon becomes heavier and
the buoyant force decreases, causing it to sink.
 Ships: Ships float because they are designed to displace
a large volume of water. The buoyant force (weight of
the displaced water) is greater than the weight of the
ship, keeping it afloat.

Important Questions:

1. An object weighs 10 N when measured on the surface of

the Earth. What would be its weight when measured on
the surface of the moon?
(a) 1.25 N
(b) 2.7 N
(c) 1.66 N
(d) 3.18 N

2. Which of the following is the unit of gravitational

constant 'G'? Options:
(a) N/kg
(b) N.m²/kg²
(c) m²/s²
(d) kg/m²

3. If the mass of one body is doubled and the distance

between two bodies is halved, the gravitational force
between them will become:
(a) 2 times
(b) 4 times
(c) 8 times
(d) 16 times

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Science Class IX Abhyasa classes

4. 4. A piece of cork floats on water due to buoyant force.

What happens if you push it further into the water?
(a) The buoyant force will increase as the cork is
immersed.
(b) The buoyant force will decrease.
(c) It will first increase and then decrease.
(d) The buoyant force will remain constant.

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