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Question
Observe the figure and answer the questions:
- State Newton's universal law of gravitation.
- If the distance between the two bodies is tripled, how will the gravitational force between them change?
- What will happen to gravitational force, if mass of one of the object is doubled?
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Solution
- According to Newton’s universal law of gravitation theory, every object in the universe attracts every other object with a definite force. This force is directly proportional to the product of the masses of the two objects and is inversely proportional to the square of the distance between them. The above figure shows two objects with masses m1 and m2 kept at a distance d from each other. Mathematically, the gravitational force of attraction between these two bodies can be written as
`Fα (m_1m_2)/d^2 or F= G (m_1m_2)/d^2`
Here, G is the constant of proportionality and is called the universal gravitational constant. - If the distance between the two bodies is tripled, the gravitational force between them would decrease by a factor of 9 (since force is inversely proportional to the square of the distance). This is because according to the law of gravitation, F ∝ `1/d^2`, so if d becomes 3d, then
`F = G(m_1m_2)/(3d^2) = G(m_1m_2)/(9d^2)` - If the mass of one of the objects is doubled, the gravitational force between them will also double. This is because the force is directly proportional to the masses of the objects. So, F ∝ m1 or F ∝ m2, which means if m1 becomes 2m1,
`F = G(2m_1m_2)/(d^2) = 2G(m_1m_2)/(d^2)`
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