Gravitation
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GRAVITATION
The discovery of the law of gravitation
The way the law of universal gravitation was discovered is often considered as the paradigm of modern scientific
technique. The major steps involved were :
The hypothesis about planetary motion given by Nicolaus Copernicus (1473–1543).
The careful experimental measurements of the positions of the planets and the Sun by
Tycho Brahe (1546–1601).
Analysis of the data and the formulation of empirical laws by Johannes Kepler (1571–1630).
The development of a general theory by Isaac Newton (1642–1727
1.1 Newton's law of Gravitation
It states that every particle in the universe attracts all other particle with a force which is directly proportional
to the product of their masses and is inversely proportional to the square of the distance between them.
If = [G = Universal gravitational constant]
Gravitational force is always attractive.
Gravitational forces are developed in the form of action and reaction pair. Hence they obey Newton's third
law of motion.
It is independent of the nature of medium between two masses.
Gravitational forces are central forces as they act along the line joining the centre of gravity of the two bodies.
Gravitational forces are conservative forces so work done by gravitational force does not depends on path.
If any particle moves along a closed path under the action of gravitational force then the work done by this
force is always zero for round the trip.
Gravitational force is weaker than the electromagnetic and nuclear forces.
Force developed between any two masses is called gravitational force and force between Earth and any body
is called force of gravity.
The total gravitational force on a particle due to a number number of particles is the resultant of the forces
of attraction exerted on the given particle due to the individual particles i.e. F F1 F2 F3 ............
® ® ® ®
= + + + It
means the principle of superposition is valid
Gravitational force holds good over a wide range of distances. It is found true from interplanetary distances
to interatomic distances.
It is a two body interaction i.e. gravitational force between the two particles is independent of the presence
or absence of other bodies or particles
A uniform spherical shell of matter attracts a particle that is outside the shell as if all its mass were concentrated at its centre
Two spherical balls of mass 10 kg each are placed 100 m apart. Find the gravitational force of attraction
between them.
Two particles of masses 1 kg and 2 kg are placed at a separation of 50 cm. Assuming that the only forces
acting on the particles are their mutual gravitation, find the initial acceleration of the heavier particle.
Two stationary particles of masses M1 and M2 are 'd' distance apart. A third particle lying on the line joining
the particles, experiences no resultant gravitational force. What is the distance of this particle from M1?
Three masses, each equal to M are placed at the three corners of a square of side a. Calculate the force
of attraction on unit mass placed at the fourth corner
Two particles each of equal mass (m) move along a circle of radius (r) under the action
m r r m
of their mutual gravitational attraction. Find the speed of each particle
Three particles, each of mass m, are situated at the vertices of an equilateral triangle of side 'a'. The only
forces acting on the particles are their mutual gravitational forces. It is intended that each particle moves
along a circle while maintaining their original separation 'a'. Determine the initial velocity that should be given
to each particle and the time period of the circular motion
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