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A stone is attached to a string of length l and is rotated in a vertical circle with the other end of the string fixed. At one instant, the stone is at the lowest point and its speed is u. What is the magnitude of the change in its velocity when it reaches the point where the string becomes horizontal? (Take g as the acceleration due to gravity)

1. √(2gl)
2. √(2(u² − gl))
3. √(u² − gl)
4. u − √(u² − 2gl)

Correct answer: √(2(u² − gl))

Solution

The correct option is derived from the conservation of mechanical energy. At the lowest point, the stone has kinetic energy due to its speed u, and as it rises to the horizontal position, some of this energy is converted into potential energy, resulting in a change in velocity that can be expressed as √(2(u² - gl)).

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