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5.Work, Energy, Power and Collision
hard
A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at 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 its velocity as it reaches a position where the string is horizontal is
A
$\sqrt {{u^2} - 2gL} $
B
$\sqrt {2gL} $
C
$\sqrt {{u^2} - gl} $
D
$\sqrt {2({u^2} - gL)} $
(IIT-1998) (AIPMT-2004)
Solution
(d) $\frac{1}{2}m{u^2} – \frac{1}{2}m{v^2} = mgL$
$⇒$ $v = \sqrt {{u^2} – 2gL} $
$|\vec v – \vec u|\, = \sqrt {{u^2} + {v^2}} = \sqrt {{u^2} + {u^2} – 2gL} = \sqrt {2({u^2} – gL)} $
Standard 11
Physics
