How the gravitational force between two objects depends on the distance between them? What happens to the gravitational force between two objects when the distance between them is doubled?


Gravitational force F between two objects is inversely proportional to the square of the distance between them, i.e.,


Gravitational force F between two objects is inversely proportional t

When the distance between two objects is doubled, the force becomes one-fourth of its original value.

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What is the importance of universal law of gravitation?


The universal law of gravitation successfully explained many phenomena occurring in nature.

Some of these phenomena are as follows:

1. The force that binds us to the earth.

2. The motion of the moon around the earth.

3. The motion of planets around the sun.

4. The tides due to the moon and the sun. 

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A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Find when and where the two stones meet?


Suppose the two stones meet at a height x from the ground, after time t from the start.


Suppose the two stones meet at a height x from the ground, after time

Hence, the two stones meet after 4 s at a height of 20 m from the ground or 80 m from the top.

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 A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) the maximum height to which it rises,
(ii) the total time it takes to return to the surface of the earth.


(i) In Cartesian sign convention, upward velocity is taken positive and acceleration due to gravity is taken negative.


(i) In Cartesian sign convention, upward velocity is taken positive a


(i) In Cartesian sign convention, upward velocity is taken positive a

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What happens to the force between two bodies, if
(i) the mass of one body is doubled?
(ii) the distance between the bodies is doubled and tripled?
(iii) the masses of both bodies are doubled?


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A ball thrown up vertically returns to the thrower after 6 s. Find:
(a) the velocity with which it was thrown up,
(b) the height, and
(c) its position after 4 s.


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