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The Earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the Earth. The velocity of a body from this platform is √v, where v is its velocity from the surface of the Earth. The value of √v is

1. 1/√2
2. 1/3
3. 1/2
4. √2

Correct answer: 1/√2

Solution

The velocity of a body at a height R from the Earth's surface is given by the formula v = √(GM/(R+h)), where h = R. Substituting h = R, the velocity becomes v = √(GM/(2R)), which is 1/√2 times the velocity at the Earth's surface (√(GM/R)).

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