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Physics · GRAVITATION
हिन्दीA projectile of mass \( m \) is projected from the surface of a fixed sphere of mass \( M \) and radius \( R \) towards another fixed sphere of mass \( 4M \) and radius \( R \), whose centre is at a distance of \( 6R \) from the centre of the first sphere. The minimum speed \( v \) required for the projectile to reach the surface of the second sphere is:
Correct answer · Option A
\( \sqrt{\frac{3GM}{5R}} \)
Explanation
The projectile needs enough energy to cross the neutral point at \( r = 2R \). Energy conservation gives \( \frac{1}{2}mv^2 - \frac{GMm}{R} - \frac{4GMm}{5R} = -\frac{GMm}{2R} - \frac{4GMm}{4R} \), yielding \( v = \sqrt{\frac{3GM}{5R}} \).
