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
2u2âgl
b
u2âgl
c
uâu2â2gl
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=u2â2gl â¦(1)This magnitude of change of velocity figure is given by |Îv|=|vâu|=v2+u2â2uvcosâ¡90â=v2+u2 ....(2)From eqs, (1) and (2), we get|Îv|=u2â2gl+u2=2u2âgl