Question

Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R . if they attract each due to gravitational force only , then the distance covered by the smaller body just before collision is [AIEEE 2003] ​

Answer 1

Since smaller ball have more acceleration in same time interval, smaller ball will cover more distance.

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Answer 2

Explanation:- Just before collision , total distance travelled by both = 12R -R - 2R = 9R

Let x is the distance travelled by block of mass M and (9R-x) The distance travelled by block of mass 5M

As the centre of mass of system doesn't change , then ,

* By conservation of mementum *

• Mx = 5M (9R - x)

• Mx = 45MR - 5Mx

• 6Mx = 45MR

• 6x = 45R

• x = 45R/6 = 7.5R

So distance covered by the smaller body just before collision is 7.5R