Chapter 9: Gravitation

Consider the Universal law of gravitation,

According to that law, the force of attraction between two bodies is

Where,

m₁ and m₂ are the masses of the two bodies.

G is the gravitational constant.

r is the distance between the two bodies.

Given that the distance is reduced to half then,

r = 1/2 r

Therefore,

F = 4F

Therefore once the space between the objects is reduced to half, then the force of gravitation will increase by fourfold the first force.

All objects fall from the top with a constant acceleration called acceleration due to gravity (g). This is constant on earth and therefore the value of ‘g’ doesn’t depend on the mass of an object. Hence, heavier objects don’t fall quicker than light-weight objects provided there’s no air resistance.

From Newton’s law of gravitation, we know that the force of attraction between the bodies is given by

The earth attracts the moon with a force same as the force with which the moon attracts the earth. However, these forces are in opposite directions. By universal law of gravitation, the force between moon and also the sun can be

Where,

d = distance between the earth and moon.

m₁ and m₂ = masses of earth and moon respectively.

According to the universal law of gravitation and Newton’s third law, we all know that the force of attraction between two objects is the same, however in the opposite directions. So the earth attracts the moon with a force same as the moon attracts the earth but in opposite directions. Since earth is larger in mass compared to that of the moon, it accelerates at a rate lesser than the acceleration rate of the moon towards the Earth. Therefore, for this reason the earth does not move towards the moon.

(i)

According to universal law of gravitation, the force between 2 objects (m₁ and m₂) is proportional to their plenty and reciprocally proportional to the sq. of the distance(R) between them.

If the mass is doubled for one object.

F = 2F, so the force is also doubled.

(ii)

If the distance between the objects is doubled and tripled

If it’s doubled

Hence,

F = (Gm₁m₂)/(2R)²

F = 1/4 (Gm₁m₂)/R²

F = F/4

Force thus becomes one-fourth of its initial force.

Now, if it’s tripled

Hence,

F = (Gm₁m₂)/(3R)²

F = 1/9 (Gm₁m₂)/R²

F = F/9

Force thus becomes one-ninth of its initial force.

(iii)

If masses of both the objects are doubled, then

F = 4F, Force will therefore be four times greater than its actual value.

The universal law of gravitation explains many phenomena that were believed to be unconnected:

(i) The motion of the moon round the earth

(ii) The responsibility of gravity on the weight of the body which keeps us on the ground

(iii) The tides because of the moon and therefore the Sun

(iv) The motion of planets round the Sun

Acceleration due to gravity is the acceleration gained by an object due to gravitational force. On Earth, all bodies experience a downward force of gravity which Earth’s mass exerts on them. The Earth’s gravity is measured by the acceleration of the freely falling objects. At Earth’s surface, the acceleration of gravity is 9.8 ms^-2 and it is denoted by ‘g’. Thus, for every second an object is in free fall, its speed increases by about 9.8 metres per second.

The gravitation force between the earth and an object is called weight. Weight is equal to the product of acceleration due to the gravity and mass of the object.

The weight of a body on the earth’s surface;

W = mg (where m = mass of the body and g = acceleration due to gravity)

The value of g is larger at poles when compared to the equator. So gold can weigh less at the equator as compared to the poles.

Therefore, Amit’s friend won’t believe the load of the gold bought.