A) \[\frac{4h}{{{R}^{2}}}\]
B) \[4h{{R}^{2}}\]
C) \[\frac{{{R}^{2}}}{4h}\]
D) \[\frac{h}{4{{R}^{2}}}\]
Correct Answer: C
Solution :
Velocity of efflux, \[{{E}^{f}}=-\frac{GMm}{2(2R+R)}\] Time taken for the range. \[[\because \,\,\text{height}\,=2R)\] Range = velocity \[={{E}_{f}}-{{E}_{i}}\] time \[\Rightarrow \] or \[\Delta E=\frac{-GMm}{6R}+\frac{GMm}{R}=\frac{5}{6}\,\frac{GMm}{R}\] \[\Rightarrow \] \[\Delta E=\frac{5}{6}\,mgR\]You need to login to perform this action.
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