1.

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?A. `5/3mgR`B. `4/3mgR`C. `5/6mgR`D. `5/4mgR`

Answer» Correct Answer - C
Total energy `E=1/2mv^(2)-(GmM)/r`
`=(GmM)/(2r)-(GMm)/r=-G(mM)/(2r)`
`r=2R=R=3R`
`E=(GmM)/(6R)`
Potential energy `=-(GMm)/R`
Minimum energy required `=1/6(GMm)/R-((-GMm)/R)=5/6(GMm)/R`


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