Physics · GRAVITATION

In the diagram shown below, two fixed solid spheres have masses \( M \) and \( 4M \) and radii \( R \), with center-to-center distance \( 6R \). At the neutral point \( N \) located along the line joining their centers, what is the distance of \( N \) from the center of sphere of mass \( M \)?

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Correct answer · Option B

\( 2R \)

At the neutral point \( N \), \( \frac{GM}{r^2} = \frac{4GM}{(6R-r)^2} \implies \frac{1}{r} = \frac{2}{6R-r} \implies 6R - r = 2r \implies r = 2R \).