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Two uniform spherical starts made of sa...

Two uniform spherical starts made of same material have radii R and 2R. Mass of the smaller planet is m. They start mmoving from rest towards each other from a large distance under mutual force of gravity. The collision between the stars is inelastic with coefficient of restitution 1/2.
The maximum separation between their centres after their first collision

A

4 R

B

6 R

C

8 R

D

12 R

Text Solution

Verified by Experts

The correct Answer is:
A
Let maximum sepration is r from conservation of energy
`U_(i)+K_(i)=U_(i)+K_(f)`
`-(G(m)(8m))/(3R)+(2)/(3)(Gm^(2))/(R )=-(G(m)(8m))/(r )+0`
`=(8Gm^(2))/(3R)+(2)/(3)(Gm^(2))/(R )=-(G8m^(2))/(r )`
`=(8)/(3R)+(2)/(3R)=(-8)/(r ) rArr (8)/(r )=(6)/(3)R rArr r = 4R`
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