Chapter - 3 Gravitation

Q&A -Ask Doubts and Get Answers

Q
Gravitation

Question:

What happens to the force between two objects, if

(i) the mass of one object is doubled?

(ii) the distance between the objects is doubled and tripled?

(iii) the masses of both objects are doubled?

Answer:

According to the Universal law of gravitation, the force of attraction between two bodies is given by:

F = G\frac{m_1m_2}{r^2}

Case (i): The mass of one object is doubled.

When the mass of one object is doubled, the new force F' is

F' = G\frac{2m_1m_2}{r^2}

F' = 2G\frac{m_1m_2}{r^2}

F' = 2F

If the mass of one object is doubled, the gravitational force is also get doubled.

Case (ii):  The distance between the objects is doubled and tripled.

When the distance between the objects is doubled then,

Distance r becomes 2r, the new force F' is given by

F' = G\frac{m_1m_2}{(2r)^2}

F' = G\frac{m_1m_2}{4r^2}

F' = \frac{1}{4}G\frac{m_1m_2}{r^2}

F' = \frac{1}{4}F

The gravitational force becomes one-fourth of its initial value.

And, when the distance between the objects is tripled then,

Distance r becomes 3r, the new force F' is given by

F' = G\frac{m_1m_2}{(3r)^2}

F' = G\frac{m_1m_2}{9r^2}

F' = \frac{1}{9}G\frac{m_1m_2}{r^2}

F' = \frac{1}{9}F

The gravitational force becomes one-ninth of its initial value.

Case (iii): The masses of both objects are doubled.

When the masses of both objects are doubled, the new force F' becomes

F' = G\frac{2m_1\times2m_2}{r^2}

F' = 4G\frac{m_1m_2}{r^2}

F' = 4F

If the masses of both objects are doubled, the gravitational force becomes four times of its initial value.


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