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

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Correct answer: D. 7.5R

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

Two spherical bodies of masses M and 5 M and radii R and 2 R...

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