Two spherical objects have masses M and 5M an | vedclass

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(D) The initial distance between the centers of the two spheres is $12R$. Collision occurs when the distance between their centers becomes equal to th

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$7.5$

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(D) The initial distance between the centers of the two spheres is $12R$. Collision occurs when the distance between their centers becomes equal to the sum of their radii,which is $R + 2R = 3R$. Therefore,the total distance covered by both objects to collide is $12R - 3R = 9R$. Since the system is in free space and only internal gravitational forces act,the center of mass of the system remains stationary. Let $x$ be the distance traveled by the smaller object (mass $M$) and $y$ be the distance traveled by the larger object (mass $5M$). From the property of the center of mass,$M x = (5M) y$. We also know that $x + y = 9R$,so $y = 9R - x$. Substituting $y$ in the equation: $M x = 5M (9R - x)$. $x = 45R - 5x$. $6x = 45R$. $x = 7.5R$.

Two spherical objects have masses $M$ and $5M$ and radii $R$ and $2R$ respectively. They are released in free space with their centers at a distance of $12R$. If they attract each other only due to gravitational force,the distance traveled by the smaller object before collision is: (in $R$)

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