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F = (Gm(1)m(2))/(r^(2)) is valid...

`F = (Gm_(1)m_(2))/(r^(2))` is valid

A

Between bodies with any shape

B

Between particles

C

Between any bodies with uniform density

D

Between any bodies with same shape

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The correct Answer is:
To determine the validity of the equation \( F = \frac{G m_1 m_2}{r^2} \), we need to analyze the context in which this equation applies. This equation is known as Newton's Law of Universal Gravitation, which describes the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \). ### Step-by-Step Solution: 1. **Understanding the Equation**: - The equation states that the gravitational force \( F \) between two masses is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. - Here, \( G \) is the gravitational constant. 2. **Identifying the Applicability**: - The law applies universally to any two bodies in the universe, regardless of their shape, size, or composition. - This means it is valid for both small and large bodies, celestial bodies (like planets and stars) and terrestrial bodies (like objects on Earth). 3. **Evaluating the Options**: - **Option 1**: Between bodies with any shape - This is correct because the law applies to all shapes. - **Option 2**: Between particles - This is too restrictive; while it applies to particles, it is not limited to them. - **Option 3**: Between any bodies with uniform density - This is incorrect; the law does not require uniform density. - **Option 4**: Between any bodies with the same shape - This is also incorrect; the law does not require bodies to have the same shape. 4. **Conclusion**: - The correct answer is **Option 1**: The equation is valid for gravitational interaction between bodies of any shape.
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