A) \[\frac{GMm}{C}\left[ \frac{1}{R}-\frac{1}{r} \right]\]
B) \[\frac{GMm}{2C}\left[ \frac{1}{R}+\frac{1}{r} \right]\]
C) \[\frac{GMm}{2C}\left[ \frac{1}{R}-\frac{1}{r} \right]\]
D) \[\frac{2GMm}{C}\left[ \frac{1}{R}+\frac{1}{r} \right]\]
Correct Answer: C
Solution :
[c] \[E=-\frac{GMm}{2r}\] \[-\frac{dE}{dt}=\frac{GMm}{2r}\frac{1}{{{r}^{2}}}\frac{dr}{dt}\] \[\int\limits_{0}^{t}{dt=-\frac{GMm}{2C}\int\limits_{r}^{R}{\frac{dr}{{{r}^{2}}};t=\frac{GMm}{2C}\left[ \frac{1}{R}-\frac{1}{r} \right]}}\]
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