Gravitation Class 9 Notes Science Chapter 9

Universal Law of Gravitation

• Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them.
• The force is along the line joining the centres of two objects.
  

Gravitational Force between two uniform objects is directed along the line joining their centres.

• Let two objects A and B of masses M and m lie at a distance of d from each other as shown in the figure.
• Let F be the force of attraction between two objects. According to the universal law of gravitation
• G is called a universal constant because its value does not depend on the nature of the intervening medium temperature or any other physical variable.
• S.I. unit of G = Nm²/kg² 
• Value of G = 6.673 × 10⁻¹¹ Nm²/kg² (Found by Henry Cavendish)

Importance of Universal Law of Gravitation

The universal law of gravitation successfully explained several phenomena:
(i) the force that binds us to the earth.
(ii) the motion of the moon around the earth.
(iii) the motion of planets around the Sun.
(iv) the tides due to the moon and the Sun.

Free fall 
When an object falls towards the earth under the gravitational force alone, we say the object is in free fall.
The velocity of a freely falling body changes and is said to be accelerated.
This acceleration is called acceleration due to gravity, denoted by ‘g’. Unit is m/s².
As F = ma                 (∵ a = g) ...(i)
F = mg                    ...(ii)
and
F = G(Mm/d²) (from Universal law of gravitation) ...(iii)
 From (ii) and (iii)
∴ mg = G(Mm/d²)
∴ g= GM/d²
M = Mass of the earth
d = Distance between the object and the earth
G = Gravitational constant If the object is placed on the earth then
d = R (R = radius of the earth)
 ...(iv)

Earth is not a sphere, it is flattened at the poles.

Hence R_p − Radius at pole and R_e − Radius at equator

∴ The value of ‘g’ is more at poles = (9.9 m/s²) and less at equator = (9.8 m/s²)

Calculation of value of g

g= G(M/R²
G = 6.67 x 10^-11 Nm²/kg²
M = 6 × 10²⁴ kg (Mass of the earth)
R = 6.4 × 10⁶ m
On substituting the given values

• Motion of objects under the influence of gravity ‘g’ does not depend on the mass of the body. All objects small, big, heavy, light, hollow or solid fall at the same rate.
•  The three equations of motion viz.
  (i) v = u + at
  (ii) s = ut + (1/2) at²
  (iii) v² – u² = 2 as is true for the motion of objects under gravity. For free fall, the value of acceleration a = g = 9.8 ms^–2.
• If an object is just let fall from a height then in that case u = 0 and a = g = 9.8 m/s².
• If an object is projected vertically upward with an initial velocity u, then a = – g = – 9.8 ms^–2 and the object will go to a maximum height h where its final velocity becomes zero (i.e., v = 0).

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Mass

The mass of an object is the measure of its inertia. It is the matter present in it. It remains the same everywhere in the universe.

Weight

The force of attraction of the earth on the object is known as the weight of the object. Its S.I. unit is Newton.
W = m × g
The weight of an object can change from one place to the other, from one planet to the other.
The weight of an object on the moon is given by the formula

W_m = weight of an object on the moon
M_m = Mass of the moon = 7.36 x 10²²
R_m = radius of the moon = 1.74 x 10⁶
G = 6.67 x 10^-11 Nm^2_/kg²

W_m = 1.474 × 10¹⁰ G × m
and W_e = 1.474 × 10¹¹ G × m
∴
∴ The weight of an object on the moon = (1/6) th the weight of an object on the earth.

Thrust

It is the net force applied in a particular direction. Its S.I. unit is N.

Pressure

• It is the force per unit area.
• Pressure = thrust / area , S.I unit = N/m²   = Pascal (pa) 

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Pressure in fluids 

• All liquids and gases are fluids, as they can flow.
• The pressure exerted by a fluid is transmitted in all directions.

Buoyancy 

• The upward force exerted by water (fluid) on the body is known as upthrust or buoyancy.
• The magnitude of the buoyant force depends on the density of the fluid.
  A − Wooden block
  B₁ − Beaker with tap water
  B₂ − Beaker with salty water
  The buoyant force exerted in B₂ is more as compared to B₁. This is because the density of B₂ water is higher.
  The object may float, sink or remain half submerged and half above water, the density of the fluid and object decides this.
  • If the density of an object is less than the fluid, then it will float on the liquid.
  • If the density of an object is more than the fluid, then it will sink in the liquid.
  • If the density of an object is the same as the density of fluid, then it will half float and half sink.

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Archimedes’ Principle

When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

Its applications are: 

(i) Used in designing ships and submarines,
(ii) In lactometers to find the purity of milk.
(iii) In hydrometer to determine the density of the liquid.

Relative Density

• Relative density = density of substance/density of water
• It has no unit.