Important Points and Formulas: Gravitation | Science Class 9 PDF Download

 Page 1


 
 
 
1 
 
GRAVITATION 
 
 
 
  
Universal Law of Gravitation 
According to Newton’s universal law of gravitation, every object in the universe attracts 
every other object with a force, which is 
 (i) Directly proportional to the product of the masses of the objects and  
 (ii) Inversely proportional to the square of the distance between their centres. 
  
    
 The SI unit of G can be obtained by substituting the unit of force, distance and mass 
in equation (iii). 
   
    or  
Newton’s third law of motion (i.e., action and reaction are always equal and opposite) 
applies to gravitational force as well.  
Kepler’s Laws of Planetary Motion 
1
st
 Law: Every planet revolves around the Sun in an elliptical orbit, with the Sun situated at 
any one of the foci of the ellipse. 
2
nd
 Law: In the elliptical orbit of the planet, the line joining the centre of the planet to the centre 
of Sun sweeps out equal areas in equal intervals of time. 
3
rd
 Law: The Square of time period of revolution of a planet around the Sun is directly 
proportional to the cube of the semi-major axis or the elliptical orbit. 
•Newton guessed the inverse square rule  using Kepler’s third law of planetary 
motion, and assuming that orbits of planets around the Sun are circular. 
Gravity is the phenomenon of attraction between Earth and any other body. Force of 
gravity,   F =  
 where M is mass of Earth and m is mass of the body at a distance r from the centre of 
Earth. 
Relation between g and G 
The relation between g and G is g =  where M is mass of Earth and R is radius of Earth. 
The value of g does not depend on mass of the body. 
Three Equations of Motion under Gravity 
  v = u + gt 
m M
d F
G
´
´
=
2
kg kg´
=
2
Nm
G
2 2
kg / Nm G =
2 2
kg Nm
-
= G
÷
÷
ø
ö
ç
ç
è
æ
µ
2
1
i.e.,
r
F
2
r
M m G
2
R
GM
Page 2


 
 
 
1 
 
GRAVITATION 
 
 
 
  
Universal Law of Gravitation 
According to Newton’s universal law of gravitation, every object in the universe attracts 
every other object with a force, which is 
 (i) Directly proportional to the product of the masses of the objects and  
 (ii) Inversely proportional to the square of the distance between their centres. 
  
    
 The SI unit of G can be obtained by substituting the unit of force, distance and mass 
in equation (iii). 
   
    or  
Newton’s third law of motion (i.e., action and reaction are always equal and opposite) 
applies to gravitational force as well.  
Kepler’s Laws of Planetary Motion 
1
st
 Law: Every planet revolves around the Sun in an elliptical orbit, with the Sun situated at 
any one of the foci of the ellipse. 
2
nd
 Law: In the elliptical orbit of the planet, the line joining the centre of the planet to the centre 
of Sun sweeps out equal areas in equal intervals of time. 
3
rd
 Law: The Square of time period of revolution of a planet around the Sun is directly 
proportional to the cube of the semi-major axis or the elliptical orbit. 
•Newton guessed the inverse square rule  using Kepler’s third law of planetary 
motion, and assuming that orbits of planets around the Sun are circular. 
Gravity is the phenomenon of attraction between Earth and any other body. Force of 
gravity,   F =  
 where M is mass of Earth and m is mass of the body at a distance r from the centre of 
Earth. 
Relation between g and G 
The relation between g and G is g =  where M is mass of Earth and R is radius of Earth. 
The value of g does not depend on mass of the body. 
Three Equations of Motion under Gravity 
  v = u + gt 
m M
d F
G
´
´
=
2
kg kg´
=
2
Nm
G
2 2
kg / Nm G =
2 2
kg Nm
-
= G
÷
÷
ø
ö
ç
ç
è
æ
µ
2
1
i.e.,
r
F
2
r
M m G
2
R
GM
2 
 
   h  = 
   = 2 gh 
 where u is initial velocity, v is final velocity after t second, h is the height covered in t 
second. 
 When a body is projected upwards, it undergoes retardation = g = – 9.8  and in 
free fall, the body has uniform acceleration g = + 9.8 . 
Mass and Weight 
• Mass of a body is the quantity of matter in the body.  
• Weight of a body is the force with which the body is attracted towards the centre 
of the Earth.  
 
Thrust and Pressure 
• Force acting normally or perpendicular to the surface is called thrust. 
• Pressure (P) is the thrust (F) per unit area of the surface, i.e., P = F/A. 
• The same force acting on a smaller area exerts a large pressure and a smaller 
pressure while acting on a larger area. 
The unit of pressure is pascal (Pa) where 1 Pa = . 
 Other units of pressure are (i) bar (ii) millibar (m bar) and (iii) atm 
    1 bar =  Pa and 1 m bar =  Pa 
   1 atmospheric pressure (1 atm)  =  
    = 101.3 k Pa = 1.013 bar 
Density and Relative Density 
Mass per unit volume of a substance is called its density, i.e., 
   density (d)  =  
The SI unit of density is  and its cgs unit is . 
Density of a substance is one of its characteristic properties and it enables us to determine 
its purity. 
Relative density of a substance is defined as the ratio of its density to that of water at 
4ºC. Being a ratio of two similar quantities, it has no unit. 
Relative density =  
Relative density of a substance is also defined as the ratio of the mass of the substance to 
the mass of an equal volume of water at 4ºC. 
2
2
1
gt ut +
2 2
u v -
2
m/s
2
m/s
2
N/m 1
5
10
2
10
Pa 10 013 . 1 N/m 10 013 . 1
5 2 5
´ = ´
) ( volume
) ( mass
V
M
3
kg/m
3
g/cm
 water of Density 
substance of Density
Page 3


 
 
 
1 
 
GRAVITATION 
 
 
 
  
Universal Law of Gravitation 
According to Newton’s universal law of gravitation, every object in the universe attracts 
every other object with a force, which is 
 (i) Directly proportional to the product of the masses of the objects and  
 (ii) Inversely proportional to the square of the distance between their centres. 
  
    
 The SI unit of G can be obtained by substituting the unit of force, distance and mass 
in equation (iii). 
   
    or  
Newton’s third law of motion (i.e., action and reaction are always equal and opposite) 
applies to gravitational force as well.  
Kepler’s Laws of Planetary Motion 
1
st
 Law: Every planet revolves around the Sun in an elliptical orbit, with the Sun situated at 
any one of the foci of the ellipse. 
2
nd
 Law: In the elliptical orbit of the planet, the line joining the centre of the planet to the centre 
of Sun sweeps out equal areas in equal intervals of time. 
3
rd
 Law: The Square of time period of revolution of a planet around the Sun is directly 
proportional to the cube of the semi-major axis or the elliptical orbit. 
•Newton guessed the inverse square rule  using Kepler’s third law of planetary 
motion, and assuming that orbits of planets around the Sun are circular. 
Gravity is the phenomenon of attraction between Earth and any other body. Force of 
gravity,   F =  
 where M is mass of Earth and m is mass of the body at a distance r from the centre of 
Earth. 
Relation between g and G 
The relation between g and G is g =  where M is mass of Earth and R is radius of Earth. 
The value of g does not depend on mass of the body. 
Three Equations of Motion under Gravity 
  v = u + gt 
m M
d F
G
´
´
=
2
kg kg´
=
2
Nm
G
2 2
kg / Nm G =
2 2
kg Nm
-
= G
÷
÷
ø
ö
ç
ç
è
æ
µ
2
1
i.e.,
r
F
2
r
M m G
2
R
GM
2 
 
   h  = 
   = 2 gh 
 where u is initial velocity, v is final velocity after t second, h is the height covered in t 
second. 
 When a body is projected upwards, it undergoes retardation = g = – 9.8  and in 
free fall, the body has uniform acceleration g = + 9.8 . 
Mass and Weight 
• Mass of a body is the quantity of matter in the body.  
• Weight of a body is the force with which the body is attracted towards the centre 
of the Earth.  
 
Thrust and Pressure 
• Force acting normally or perpendicular to the surface is called thrust. 
• Pressure (P) is the thrust (F) per unit area of the surface, i.e., P = F/A. 
• The same force acting on a smaller area exerts a large pressure and a smaller 
pressure while acting on a larger area. 
The unit of pressure is pascal (Pa) where 1 Pa = . 
 Other units of pressure are (i) bar (ii) millibar (m bar) and (iii) atm 
    1 bar =  Pa and 1 m bar =  Pa 
   1 atmospheric pressure (1 atm)  =  
    = 101.3 k Pa = 1.013 bar 
Density and Relative Density 
Mass per unit volume of a substance is called its density, i.e., 
   density (d)  =  
The SI unit of density is  and its cgs unit is . 
Density of a substance is one of its characteristic properties and it enables us to determine 
its purity. 
Relative density of a substance is defined as the ratio of its density to that of water at 
4ºC. Being a ratio of two similar quantities, it has no unit. 
Relative density =  
Relative density of a substance is also defined as the ratio of the mass of the substance to 
the mass of an equal volume of water at 4ºC. 
2
2
1
gt ut +
2 2
u v -
2
m/s
2
m/s
2
N/m 1
5
10
2
10
Pa 10 013 . 1 N/m 10 013 . 1
5 2 5
´ = ´
) ( volume
) ( mass
V
M
3
kg/m
3
g/cm
 water of Density 
substance of Density
 
 
3 
 
Pascal’s law states that the pressure applied at any place to an enclosed mass of a fluid is 
transmitted equally in all directions and it acts undiminished at every point of the fluid and on 
the walls of the container.