Rod B sticks to rod A on collision. Collision takes place on horizontal plane. Rod-A is hinged O. Friction is absent every where.

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Rod $B$ sticks to rod $A$ on collision. Collision takes place on horizontal plane. Rod- $A$ is hinged $O$ . Friction is absent every where.

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Velocity of centre of mass of system just after collision is $\sqrt{\frac{9}{40}} v_{0}$

Angular velocity of system just after collision is $\frac{2 v_{0}}{5 L}$

Kinetic energy of system just after collision is $\frac{9}{40} m v^{2}$

Centre of mass of system is at a distance of $\frac{\sqrt{10} L}{4}$ from $O$

answer is B, C.

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Detailed Solution

Conservation of Angular momentum about hinge

$m v_{0} L = I ω I = \frac{5}{3} m L^{2}, ω = \frac{3 v_{0}}{5 L} K E = \frac{1}{2} I ω^{2} r_{c} = \sqrt{{(\frac{3 L}{4})}^{2} + {(\frac{L}{4})}^{2}} = \frac{\sqrt{10} L}{4}$

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