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A body is released from rest at a point located a distance R0 from the Earth’s centre. If it falls to the Earth’s surface, its speed on reaching the surface will be (R = radius of the Earth):

1. 2GM(1/R - 1/R0)
2. √(2GM(1/R0 - 1/R))
3. GM(1/R - 1/R0)
4. √(2GM(1/R - 1/R0))

Correct answer: √(2GM(1/R - 1/R0))

Solution

The correct option represents the final speed of the body as it falls under the influence of gravity, derived from energy conservation principles. It calculates the kinetic energy gained from the gravitational potential energy lost as the body moves from a distance R0 to the Earth's surface.

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