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one end an ideal spring is fixed at point at point O and end is attached to a small disc of mass m which is given an initial velocity $v_{0}$ perpendicular to its length on a smooth horizontal surface. If the maximum elongation of the spring is $\frac{l_{0}}{4}$ then ( $l_{0}$ =natural length=stiffness of the spring)

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Velocity at maximum elongation is $\frac{{4v}_{0}}{5}$

Velocity at maximum elongation is $\frac{{3v}_{0}}{5}$

$v_{0} = \frac{5 l_{0}}{12} \sqrt{\frac{k}{m}}$

$v_{0} = \frac{l_{0}}{12} \sqrt{\frac{k}{m}}$

answer is A, C.

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Detailed Solution

$V_{0} l_{0} = V (\frac{5 l_{0}}{4}), V = \frac{4 v_{0}}{5}, \frac{1}{2} m v_{0}^{2} = \frac{1}{2} m v^{2} + \frac{1}{2} k {(\frac{l_{0}}{4})}^{2}$

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