A) \[-\frac{GMm}{R}\left[ \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{5}} \right]\]
B) \[\frac{GMm}{R}\times \frac{1}{\sqrt{5}}\]
C) \[\frac{GMm}{R}\left[ \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{5}} \right]\]
D) \[\frac{GMm}{R}\left[ \frac{1}{\sqrt{10}} \right]\]
Correct Answer: C
Solution :
PE of the system when point mass is at A, is \[{{U}_{i}}=-\frac{GMm}{\sqrt{2}R}\] PE of system when point mass is at B, is \[{{U}_{f}}=-\frac{GMm}{\sqrt{5}R}\] Work done by gravity force on point mass as it moves from A to B, is \[{{W}_{gravitational}}=-dU=-({{U}_{f}}-{{U}_{i}})\] \[=\frac{GMm}{R}\left[ \frac{1}{\sqrt{5}}-\frac{1}{\sqrt{2}} \right]\] From work-energy theorem, \[dK=0={{W}_{grav.}}+{{W}_{ext.}}\] \[{{W}_{ext.}}=-{{W}_{grav.}}\] \[=\frac{GMm}{R}\left[ \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{5}} \right]\]
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