Question

A satellite of mass is launched vertically upwards with an initial speed from the surface of the earth. After it reaches height R(R= radius of the earth), it ejects a rocket of mass so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ( is the gravitational constant; is the mass of the earth) :

A

B

C

D

Hard
Solution
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Correct option is B)


As the satellite is launched vertically, the final velocity of the satellite as a whole will be radial. Now applying energy conservation between and . Taking final velocity of the whole satellite at point to be .






(Radial)
Now as the satellite reached it has only radial velocity , no tangential velocity.
Now, as the satellite ejects the recket the final velocity of satellite becomes only tangential as it starts moving in circular orbit.

Let the rocket has velocity in radial direction and tangential direction.
Applying momentum conservation in tangential direction.

(at radius 'r' in circular orbit)

and will have opposite direction so is negative
By KE at radius

Now applying conservation of momentum in radial direction.


Net KE of rocket


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