CBSE Class 9 Physics, Gravitation

Class IX Science
Notes for Gravitation
Facts that Matter
•  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.
     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 intervening medium or 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
    Universal law of gravitation successfully explained several phenomena like:
          (i) the force that binds us to the earth.
          (ii) the motion of 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 down towards the earth under the gravitational force alone, we say the object is in free fall.
    This acceleration is called acceleration due to gravity, denoted by ‘g’. Unit is m/s2.
    As F = ma        (a = g)        ...(i)
        F = mg                            ...(ii)
    
    M = Mass of the earth
    d = Distance between the object and the earth
    G = Gravitational constant
    If the object is place on the earth then d =R
    (R = radius of the earth)
    
    Earth is not a sphere it is flattened at poles.
    Calculation of value of g
    
    G = 6.67 × 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 same rate.
•  The three equation of motion viz.
    
    (iii) v2 – u2 = 2as are true for motion of objects under gravity.
          For free fall, value of acceleration a = g = 9.5 ms–2.
•  If an object is just let fall from a height then in that as 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).
•  Mass: 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.
    Weight of an object on moon is given by the formula
          
    Wm = weight of an object on moon
    Mm = mass of the moon = 7.36 × 1022
    Rm = radius of the moon = 1.74 × 106
          G = 6.67 × 10–11 Nm2/lg2
    
    ∴ Weight of an object on moon th the weight of an object on the earth.