Two spherical bodies of mass M and 5M & radii R & 2R respectively are… | JEE Main 2003 (AIEEE)

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Newton's Law of Gravitation

Two spherical bodies of mass $M$ and $5M$ & radii $R$ & $2R$ respectively are released in free space with initial separation between their centers equal to $12R$ . If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

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Answer: (c)

Only internal forces act, so the centre of mass stays fixed.
They collide when the centres are $R + 2R = 3R$ apart, so together they move $12R - 3R = 9R$ .
Distances are inversely proportional to masses: $\frac{x_1}{x_2} = \frac{5M}{M} = 5$ .
$x_1 = \frac{5}{6} \times 9R = 7.5R$
So the answer is (c) $7.5R$ .

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Newton's Law of Gravitation question from JEE Main 2003 (AIEEE)

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