A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R(R= radius of the earth), it ejects a rocket of mass 10m so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth) :
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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 A and B. Taking final velocity of the whole satellite at point B to be V.
Now as the satellite reached B it has only radial velocity v, 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 Vr in radial direction and VT tangential direction.
Applying momentum conservation in tangential direction.
⇒0=10−mVT+109mVsatellite (at radius 'r' in circular orbit)
Vsatellite and VT will have opposite direction so VT is negative
By KE at radius 2RVsatellite=RGM
Now applying conservation of momentum in radial direction.