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F=(Gm1m2)/r^2 is valid...

`F=(Gm_1m_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 conditions under which this equation holds true. ### Step-by-Step Solution: 1. **Understanding the Equation**: The equation \( F = \frac{G m_1 m_2}{r^2} \) is known as Newton's law of universal gravitation. Here, \( F \) is the gravitational force between two masses \( m_1 \) and \( m_2 \), \( r \) is the distance between the centers of the two masses, and \( G \) is the gravitational constant. 2. **Identifying the Variables**: - \( m_1 \) and \( m_2 \) are the masses of the two objects. - \( r \) is the distance between the centers of the two masses. - \( G \) is a constant that quantifies the strength of the gravitational force. 3. **Conditions for Validity**: The equation is valid under the following conditions: - The masses \( m_1 \) and \( m_2 \) can be any objects, regardless of their shape or density. - The distance \( r \) must be measured from the center of mass of the two objects. 4. **Analyzing the Options**: - **Option A**: Between bodies with any shape - This is valid because the law applies universally to all shapes. - **Option B**: Between particles - This is also valid since particles can be considered as point masses. - **Option C**: Between any bodies with uniform density - This is valid but not exclusive; it applies to more than just uniform density bodies. - **Option D**: Between any bodies with the same shape - This is not a requirement for the validity of the equation. 5. **Conclusion**: Since the equation is valid for any shape of bodies, the correct answer is **Option A**: between bodies with any shape.
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