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Q.

Consider two satellites A and B of equal mass m,moving in same circular orbit about earth. but in opposite as shown in figure. The orbital radius is r. The satellites undergoes a collision which is perfectly inelastic. Which is perfectly inelastic. For this situation , mark out the correct statements (s)

[Take mass of earth as M

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a

The total energy of the two satellites plus earth system just before collision is -2GMmr

b

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

c

The total energy of the satellites plus earth system just before collision is -GMmr

d

The total energy of two satellites plus earth system just after collision is -2GMmr

answer is A, C, D.

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Detailed Solution

Just before collision, the total energy of two satellites is , 

E = -GMm2r -GMm2r-GMmr

Let orbital velocity is v1 then from momentum conservation

mv-mv=2m×v1  v1 =0

As velocity of combined mass just after collision is zero, the combined mass will far towards earth. At this instant , the total energy of the system only consist of the gravitational potential energy given by U =- GM ×2mr

 

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