Three small balls A, B and C of same mass m are fixed by massless rods at the vertices of equilateral triangle with side L. The system is placed on a smooth horizontal surface and set m rotation about the stationary COM with angular speed $ω .$ At a certain instant ball B breaks off the system with a velocity ${\vec{v}}_{B}$ as shown in diagram where $| {\vec{v}}_{B} | = \frac{2 ω L}{\sqrt{3}} .$

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The speed of A just after B breaks off is $\frac{V_{B}}{2} .$

The COM of A and C moves with a velocity $\frac{- {\vec{v}}_{B}}{2} .$

The tension in rod connecting A and C after B breaks off is $m ω^{2} \frac{l}{2} .$

The speed of A, after a time $\frac{π}{ω}$ after B breaks off is $\frac{\sqrt{19}}{6} ω l .$

answer is A, C.

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Detailed Solution

$m {\vec{v}}_{B} + 2 m {\vec{v}}_{A C} = 0, {\vec{v}}_{A C} = \frac{- {\vec{v}}_{B}}{2} .$

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