Two spherical bodies of mass M and 5M and rad | vedclass

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(D) The initial distance between the centres of the two bodies is $12\,R$. Collision occurs when the distance between their centres is equal to the su

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$7.5$

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(D) The initial distance between the centres of the two bodies is $12\,R$. Collision occurs when the distance between their centres is equal to the sum of their radii,which is $R + 2R = 3\,R$.The total distance covered by both bodies relative to each other until collision is $12\,R - 3\,R = 9\,R$.Since the bodies move under mutual gravitational attraction only,the position of their centre of mass remains stationary. Let $x$ be the distance covered by the smaller body (mass $M$) and $y$ be the distance covered by the larger body (mass $5M$).From the property of the centre of mass,$M x = (5M) y$.We also know that $x + y = 9\,R$,which implies $y = 9\,R - x$.Substituting $y$ into the first equation: $M x = 5M(9\,R - x)$.Dividing by $M$: $x = 5(9\,R - x) = 45\,R - 5x$.$6x = 45\,R$,which gives $x = \frac{45\,R}{6} = 7.5\,R$.

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