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  4. Energy required to move a body of mass m from an orbit of radius 2R to 3R is:

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Q. Energy required to move a body of mass m from an orbit of radius 2R to 3R is:

JamiaJamia 2005

Solution:

Gravitational potential energy of body will be $ E=\frac{G{{M}_{e}}m}{r} $ where $ {{m}_{e}}= $ mass of earth, $ m= $ mass of the body, $ R= $ radius of earth At $ r=2R, $ $ {{E}_{1}}=-\frac{G{{M}_{e}}m}{r} $ At $ r=2R, $ $ {{E}_{2}}=-\frac{G{{M}_{e}}m}{(3R)} $ Energy required to move a body of mass m from an orbit of radius 2R to 3R is $ \Delta E=\frac{G{{M}_{e}}m}{R}\left[ \frac{1}{2}-\frac{1}{3} \right] $ $ =\frac{G{{M}_{e}}m}{6R} $