When two identical spheres each of radius r are kept in contact with each other, then the force of attraction between the two spheres is proportional to
- $r^{2}$
- $r^{4}$
- $r^{6}$
- $r^{-2}$
- $r^{-4}$
The Correct Option is D
Solution and Explanation
The force of attraction between two identical spheres is governed by Newton's law of gravitation, which states that the gravitational force \( F \) between two point masses (or spheres) is given by:
\[ F = \frac{G m_1 m_2}{r^2} \] Where: - \( F \) is the gravitational force, - \( G \) is the gravitational constant, - \( m_1 \) and \( m_2 \) are the masses of the two spheres, - \( r \) is the distance between the centers of the two spheres. Since the two spheres are identical, their masses are the same, and the force of attraction becomes: \[ F = \frac{G m^2}{r^2} \] From this equation, we can conclude that the force of attraction between the two spheres is inversely proportional to the square of the distance between them, which is \( r^{-2} \).
Correct Answer:
Correct Answer: (D) \( r^{-2} \)
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