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Q.

One end of an ideal spring is fixed at point O and other end is attached to a small disc of mass m which is given an initial velocity v0  perpendicular to its length on a smooth horizontal surface. If the maximum elongation of the spring is  l04  then ( l0 = natural length, k = stiffness of the spring) (initially the spring is in it’s natural length)

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a

Velocity at maximum elongation is 4v05

b

Velocity at maximum elongation is 3v05

c

v0=5l012km

d

v0=l012km

answer is A.

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Detailed Solution

According to Conservation of Angular Momentum  m×v0×l0=m×v×l0+l04⇒v=4v05According to conservation energy 12mv02=12mv2+12kx2⇒mv02=m4v052+kl042⇒v0=5l012km
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