AP EAMCET · PHYSICS · Gravitation
Two solid spheres each of radius ' \(R\) ' made of same material are placed in contact with each other. If the gravitational force acting between them is F, then
- A \(F \alpha R^4\)
- B \(F \alpha R^3\)
- C \(F \alpha R^2\)
- D \(F \alpha R\)
Answer & Solution
Correct Answer
(A) \(F \alpha R^4\)
Step-by-step Solution
Detailed explanation
\( m = \rho V = \rho \frac{4}{3}\pi R^3 \) \( r = 2R \) \( F = G \frac{m^2}{r^2} = G \frac{(\rho \frac{4}{3}\pi R^3)^2}{(2R)^2} \) \( F = G \frac{\rho^2 (\frac{4}{3}\pi)^2 R^6}{4R^2} \) \( F \propto R^{6-2} \) \( F \propto R^4 \)
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