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Question

The escape velocity for a planet is ve. A particle is projected from its surface with a speed v. For this particle to move as a satellite around the planet,

A
ve2<v<ve
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B
ve2<v<ve
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C
ve<v<2ve
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D
ve2<v<ve2
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Solution

The correct option is B ve2<v<ve
The minimum velocity for sattelite is at the nearest possible orbit, i.e., very near to the earth's surface.
So to launch sattelite to orbit very near to the earth's surface,
mg=mv2/Rv=gR=GM/R=ve/2
The maximum velocity for sattelite to orbit around earth is the escape velocity, ve.
So, ve/2<v<ve

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