Chapter - 3 Gravitation

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Q
Gravitation

Question:

How does the force of gravitation between two objects change when the distance between them is reduced to half ?

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} ----(1)

Where,

m_1 and m_2 are the masses of the two bodies, G is the gravitational constant and r is the distance between the two bodies.

Given that the distance is reduced to half then,

Distance = \frac{r}{2}

The new force F' when the distance becomes half is given by

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

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

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

From equation (1)

F' = 4F

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


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