Notes for Gravitation

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

S.I. unit of G = Nm^{2}/kg^{2}

Value of G = 6.673 � 10^{–11} Nm^{2}/kg^{2}

(Found by Henry Cavendish)

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.

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/s^{2}.

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} Nm^{2}/kg^{2}

M = 6 × 10^{24} kg (Mass of the earth)

R = 6.4 × 10^{6} 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.

(iii) v^{2} – u^{2} = 2as are true for motion of objects under gravity.

For free fall, value of acceleration a = g = 9.5 ms^{–2}.

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

W_{m} = weight of an object on moon

M_{m} = mass of the moon = 7.36 × 10^{22}

R_{m} = radius of the moon = 1.74 × 10^{6}

G = 6.67 × 10^{–11} Nm^{2}/lg^{2}

∴ Weight of an object on moon th the weight of an object on the earth.