Gravitation

The universal law of gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

Mathematically:
F = G × (m₁m₂) / r²

The gravitational force between the earth and an object is given by:

F = G × (M × m) / R²

where:
• M = mass of the earth
• m = mass of the object
• R = radius of the earth

The acceleration of free fall is the acceleration produced in a body when it falls freely under the influence of gravity alone.

Its value near the surface of the earth is approximately:
g = 9.8 m s⁻²

The gravitational force with which the earth attracts an object towards its centre is called the weight of the object.

The weight of an object does not change significantly as it falls because the value of acceleration due to gravity remains nearly constant near the earth’s surface.

The value of g varies due to:

• Change in the radius of the earth at different latitudes
• Rotation of the earth
• Altitude above sea level

Hence, g is maximum at the poles and minimum at the equator.

Mass is the amount of matter contained in a body.

SI unit of mass is kilogram (kg).

Mass remains the same everywhere and does not depend on gravity.

Weight is the gravitational force acting on a body due to the earth.

It is given by: W = mg

SI unit of weight is newton (N).

The acceleration due to gravity on the moon is about one-sixth that on the earth.

Since weight is directly proportional to gravity (W = mg), the weight of an object on the moon becomes one-sixth of its weight on earth.

The weight of a body increases when it is taken from the equator to the poles because the value of g is greater at the poles than at the equator.