Gravitation

Each and every massive body attracts each other by virtue of their masses. This phenomenon is called gravitation.

Newton’s Law of Gravitation

The gravitational force acting between two point objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Gravitational force (F) = (Gm₁ m₂)/r²

where, G is universal gravitational constant. Its value is 6.67 × 10-¹¹ N –m²kg^(-2).

Gravitational force is a central as well as conservative force.

Acceleration Due to Gravity of Earth

The uniform acceleration produced in a freely falling body due to the earth’s gravitational pull, is called acceleration due to gravity, g = GM/R²

where, M = mass of the earth, R = radius of the earth.

The value of g changes slightly from place to place but its value near the earth’s surface is 9.8 ms^(-2).

Gravitational force is the weakest force in nature. It is 10³⁶ times smaller than electrostatic force and 10³⁸ times smaller than nuclear force.

Factors Affecting Acceleration due to Gravity

Shape of Earth - Earth is not completely spherical its radius at equator is approximately 42 km greater than its radius at poles.

The value of g is maximum at poles and minimum at equator.

There is no effect of rotation of the earth at poles and maximum at equator.

Effect of Altitude - g decreases with altitude.

Effect of Depth - g decreases with depth and becomes zero at centre of the earth.

Mass and Weight

The mass of a body is the quantity of matter contained in it. It is a scalar quantity and its SI unit is kg.

Mass is measured by an ordinary equal arm balance.

Mass of a body does not change from place to place and remains constant.

The weight of a body is the force with which it is attracted towards the centre of the earth. Weight of a body (w) = mg

The centre of gravity of a body is that point at which the whole weight of the body appears to act.

The centre of gravity of a body can be inside the material of the body or outside it. It is a vector quantity and its SI unit is newton (N). It is measured by a spring balance. Weight of a body is not constant, it changes from place to place.

Weight of a Body in a Lift

When lift is rest or in uniform motion – The weight recorded in spring balance (i.e. apparent weight) is equal to the real weight of the body w = mg.

When lift is accelerating upward – The weight recorded in spring balance is greater than then real weight of the body w’ = m(g + a)

When lift is accelerating downward – The weight recorded in spring balance is smaller than the real weight of the body w’ = m(g – a).

When lift is falling freely under gravity – The apparent weight of the body

w' = m (g – g) (∵ a = g)

w’ = 0

Therefore, body will experiences weightlessness.

Weight of a Body at the Moon

As mass and radius of moon is lesser than the earth, so the force of gravity at the moon is also less than that of the earth. It’s value at the moon’s surface is g/6.