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Revision: Gravitation Science English Medium Class 9 CBSE

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Definitions [10]

Definition: Gravitation

"Every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The direction of the force is along the line joining the particles."

or

The force by which the Earth attracts objects towards its centre is called gravitational force.

Definition: Universal Law of Gravitation

"Every particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them."

Define acceleration due to gravity.

The acceleration produced in a body under the influence of the force of gravity alone is called acceleration due to gravity.

Definition: Acceleration Due to Gravity

The gravitational force due to the earth on a body results in its acceleration. This is called acceleration due to gravity and is denoted by ‘g’.

Definition: Weight

The weight of an object is defined as the force with which the earth attracts the object.

Definition: Mass

Mass is the amount of matter present in the object. The SI unit of mass is kg.

Define thrust.

The force which produces compression is called thrust. Its S.I unit is the newton.

What is the unit of relative density?

UNIT OF RELATIVE DENSITY: No units since it is a pure ratio.

Define the term Density of a substance.

Density of a substance is defined as “Mass per Unit volume”.

Density [d]=`"mass  of the substance"/"volume of the substance"`

d=`m/v`

Define the term relative density of a substance.

RELATIVE DENSITY: “is the ratio of the density of a substance to the density of water at 4° C.”
Or
RELATIVE DENSITY “is the ratio of the mass of the substance to the mass of an equal volume of water at 4° C.”

Formulae [3]

Formula: Gravitation

Newton’s Universal Law of Gravitation:
F = \[G\frac{m_1m_2}{r^2}\]

where:

  • F = Gravitational force between two objects
  • m1,m2 = Masses of the two objects
  • r = Distance between the centers of the two masses
  • G = Universal gravitational constant = 6.67×10−11 Nm2/kg2
Formula: Universal Law of Gravitation

The gravitational force of attraction (F) between two bodies of mass m1 and m2 separated by a distance r is:

\[\mathbf{F} = \mathbf{G}\frac{m_1 m_2}{r^2}\]
  • F: Gravitational Force of attraction (in Newtons, N).

  • \[m_1, m_2\]: Masses of the two objects (in kilograms, kg).

  • r (or d in the first part): Distance between the two objects (in meters, m).

  • G: The constant of proportionality, called the Universal gravitational constant.

    • Value in SI units: \[G=6.67\times10^{-11}\mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2\]

    • Dimensions: \[[G]=[\mathrm{L}^3\mathrm{M}^{-1}\mathrm{T}^{-2}]\]

Formula: Acceleration due to gravity

The value of the acceleration due to gravity (g) on the surface of the Earth is given by the formula:

\[g = \frac{G M}{R^2}\]

Where:

  • g = Acceleration due to gravity (in m/s²).
  • G = Newton's Universal Gravitational Constant (≈ 6.67 × 10⁻¹¹ N · m² / kg²).
  • M = Mass of the Earth (≈ 6 × 1024 kg).
  • R = Radius of the Earth (≈ 6.4 × 10⁶ m).

Key Points

Key Points: Newton's Universal Law of Gravitation
  • Every object attracts every other with a gravitational force.
  • Force increases with mass — more mass means a stronger pull.
  • Force decreases with distance — doubling the distance halves the force.
  • A force acts along the line joining the centres (or centres of mass) of the two bodies.
Key Points: Free Fall
  • Free fall occurs when an object moves only under the influence of gravity, with no other forces acting on it.
  • In free fall, initial velocity (u) = 0 and acceleration = g (acceleration due to gravity).
  • The equations of motion for free fall are:
    v = gt
    s = \[\frac {1}{2}\]gt2
    v2 = 2gs
  • True free fall occurs in a vacuum, as air resistance affects motion on Earth.
  • The Moon and satellites are in free fall because they move only under Earth’s gravitational field.
 
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