A launching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R. If the satellite is intended to move in a circular orbit of radius 7R, the minimum energy required to be spent by the launching vehicle on the satellite is (Gravitational constant = G) [Manipal 2012]
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a
GMmR
b
13GMm14R
c
GMm7R
d
GMm14R
answer is B.
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Detailed Solution
The energy of artificial satellite at the surface of the earth,E1=-GMmRWhen the satellite is intended to move in a circular orbit of radius 7R, then energy of artificial satellite,E2=-12GMm7RThe minimum energy required,E=E2-E1=GMmR-12GMm7R=14GMm-GMm14R=13GMm14R