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

Step-by-step solution

Let at O there will be a collision. If smaller sphere moves x distance to reach at O , then bigger sphere will move a distance of (9 R-x) . aligned F & = G M 5 M (12 R-x)^2 a_ small & = F M = G 5 M (12 R-x)^2 a_ big & = F 5 M = G M (12 R-x)^2 x & = 1 2 a_ small t^2= 1 2 G 5 M (12 R-x)^2 t^2 (i) (9 R-x) & = 1 2 a_ big t^2= 1 2 G M (12 R-x)^2 t^2 (ii) aligned Thus, dividing Eq. (i) by Eq. (ii), we get x 9 R-x =5 aligned & x=45 R-5 x & 6 x=45 R & x=7.5 R & aligned