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Gravitation




Universal Law of Gravitation

  • Universal Law of gravitation was formulated by Sit Issac Newton.
  • It states that
    Every body in universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of distance between them. The force acts along the line joining the two bodies
  • To understand that let us consider two objects of masses $M$ and $m$ that lie at a distance $r$ from each other as shown below in the figure
  • Let $F$ be the force of attraction between two objects $P$ and $Q$.
  • Now according to the universal law of gravitation as stated earlier , this force $F$ is proportional to the product of masses of objects $P$ and $Q$ that is
    $F \propto M \times m$              (1)
    and the force is inversely proportional to the square of distance between these two objects that is
    $F \propto \frac{1}{{{r^2}}}$             (2)
  • Combining both equations (1) and (2) we get
    $F \propto \frac{{Mm}}{{{r^2}}}$             (3)
    or
    $F = G\frac{{Mm}}{{{r^2}}}$             (4)
    Here G is the constant known as Universal Gravitational constant.
  • SI unit of gravitational constant G is $N{m^2}K{g^{ - 2}}$
  • Value of G was first found by Henry Cavendish (1731-1810) and it is
    $G = 6.673 \times {10^{ - 11}}N{m^2}K{g^{ - 2}}$

Important Characteristics of Gravitational forces

  • the gravitational force is a central force that is It acts along the line joining the centers of two bodies.
  • it is a long range force. The gravitational force is effective even at large distances.
  • It is a conservative force. This means that the work done by the gravitational force in displacing a body from one point to another is only dependent on the initial and final positions of the body and is independent of the path followed.
  • Unlike electrostatic and magnetic forces, the gravitational force is always attractive.

Why is this Universal Law of Gravitation so important

  • It is the force that is responsible for binding us to Earth.
  • It is responsible for the motion of moon around the earth
  • It is responsible for the motion of planets around the sun
  • The tides formed by rising and falling of water level in the ocean are due to the gravitational force exerted by both sunand moon on the earth.




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