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Consider two satellites A and B of equal...

Consider two satellites A and B of equal mass m, moving in the same circular orbit about the earth, but in opposite sense as shown in figure. The orbital radius is R. The satellite undergo a collision which is perfectly inelastic. For this situation, mark out the correct statements. [Take mass of earth as M]

A

The total energy of the satellite plus earth's system before collision is `-(GMm)//r`.

B

The total energy of the two satellites plus earth system just after collision is `-(2GMm)//r`.

C

The total energy of the two satellites plus earth system just after collision `-(GMm)//2r`.

D

The combined mass (two satellites) will fall towards the earth just after collision.

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Just before collision, the total energy of satellites is
`E=-(GM m)/(2r)-(GM m)/(2r)=-(GM m)/(r )`
Let the orbital velocity be `v_(1)`. Then from momentum conservation,
`mv-mv=2mv_(1)`
`rArr v_(1)=0`
As velocity of combined mass just after collision is zero, the combined mass will fall towards the earth. At this instant, the total energy of the system only consists of the gravitational potential energy given by
`U=(-GMxx2m)/(r )=(-2GM m)/(r )`.
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