A stone is tied to a string of length l and is whirled in

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A stone is tied to a string of length l and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is

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

Correct Option: B

W_mg = ∆K
⇒ – mgl = ½ mv² – ½ mu²
or, mv² = m( u² – 2gl )
or , v^{^→} = √u² - 2gl ĵ
u^{^→} = uî

∴ v^{^→} - u^{^→} = √u² - 2gl ĵ - uî
∴ | v^{^→} - u^{^→} | = [ (u² - 2gl) + u² ]^{1 / 2} = √2(u² - gl)