A) \[\sqrt{2gR}\]
B) \[\sqrt{gR}(\sqrt{2}-1)\]
C) \[\sqrt{\frac{gR}{2}}\]
D) \[\sqrt{gR}\]
Correct Answer: B
Solution :
The escape speed \[({{v}_{e}})\]of the satellite is \[\sqrt{2g(R+h)}\simeq \sqrt{2gR}\] \[(h<<R)\] The orbital speed \[({{v}_{0}})\]of the satellite at height h is \[\sqrt{g(R+h)}\simeq \sqrt{gR}\] Hence, the minimum increase in speed so that the satellite could escape is \[\sqrt{2gR}-\sqrt{gR}=\sqrt{gR}(\sqrt{2}-1)\]You need to login to perform this action.
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