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The escape velocity of a sphere of mass m is given by (G = Universal gravitational constant; M = Mass of the earth and Rₑ = Radius of the earth):

1. √(GM/Rₑ)
2. √(2GM/Rₑ)
3. √(2GMm/Rₑ)
4. √(2GM + Rₑ)

Correct answer: √(2GM/Rₑ)

Solution

The escape velocity is derived from equating the kinetic energy required to escape the gravitational potential energy of the Earth. The formula is v = √(2GM/Rₑ), where G is the gravitational constant, M is the Earth's mass, and Rₑ is the Earth's radius.

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