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Physics · GRAVITATION
हिन्दीTwo uniform solid spheres of radii \( R \) having masses \( M \) and \( 4M \) have their centers separated by \( 6R \). A particle of mass \( m \) is projected from the surface of sphere \( M \) directly towards the sphere of mass \( 4M \). The minimum projection speed required to reach the surface of the second sphere is:
Correct answer · Option 1
\( \sqrt{\frac{3GM}{5R}} \)
Explanation
Neutral point occurs where \( \frac{GM}{r^2} = \frac{4GM}{(6R-r)^2} \implies r = 2R \). Conserving energy from surface of \( M \) to neutral point: \( \frac{1}{2}mv^2 - \frac{GMm}{R} - \frac{4GMm}{5R} = -\frac{GMm}{2R} - \frac{4GMm}{4R} \implies v^2 = \frac{3GM}{5R} \implies v = \sqrt{\frac{3GM}{5R}} \).
