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Q.

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

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a

2u2−gl

b

u2−gl

c

u−u2−2gl

d

2gl

answer is A.

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Detailed Solution

Applying the law of conservation of energy at points B and A, we have12mu2=12mv2+mglor      V=u2−2gl        …(1)This magnitude of change of velocity figure is given by |Δv|=|v−u|=v2+u2−2uvcos⁡90∘=v2+u2       ....(2)From eqs, (1) and (2), we get|Δv|=u2−2gl+u2=2u2−gl
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