A satellite is to be launched in a circular orbit of radius ro around a planet of radius R For this two stage rocket is to be

Question

A satellite is to be launched in a circular orbit of radius ro around a planet of radius R For this two stage rocket is to be used First stage rocket is used to lift the satellite vertically up to the desired height ro measured from the center C of the planet after launching it from a launch point P Distance of launch point P from centre of the planet is rL Launch point P lies inside the tunnel as shown in the figure Second stage rocket is used to impart it a tangential velocity so as to put it in a circular orbit Let E and E2 are the energies delivered by the first and second stage of the rocket Assume that the mass of the rocket is negligible with respect to the mass of the planet and atmospheric resistance to be zero List I gives 4 values of ro and rL and List Il gives magnitude of some quantity ions 1 II III IV List I 10 R L To L R To 4R L R 2 3R 2 L R To 4R 10 00 2 correct match for P I S II T III U IV P I P II Q III T IV S I S II T III R IV P List II R 7 2 1 Q 1 11 6 S 2 T 6 U 8 C R E E for the values of ro and rL given in List I is ro

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