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With what velocity should a particle be projected so that its height becomes equal to radius of earth?

1. (GM/R)^(1/2)
2. (8GM/R)^(1/2)
3. (2GM/R)^(1/2)
4. (4GM/R)^(1/2)

Correct answer: (4GM/R)^(1/2)

Solution

To reach a height equal to the radius of the Earth, the total energy at the surface (kinetic + potential) must equal the potential energy at twice the Earth's radius. Solving for the velocity gives v = sqrt(4GM/R).

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