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Two point masses $A$ and $B$ each of $1 k g$ joined by $1 m$ rod (light) translates on horizontal surface as shown in figure. A particle of mass $1 k g$ at rest on horizontal surface sticks to ball as it collides with ball $A .$ Then

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Linear speed of a ball $A$ just after collision is $2 m / s$

Linear speed of ball $B$ just after collision is $4 m / s$

Velocity of centre of mass of system is $8 / 3 m / s$

Angular speed of system about centre of mass after collision $2 r a d / s$

answer is A, B, C, D.

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Detailed Solution

$1 \times 4 = 2 V \Rightarrow v = 2 \frac{m}{s} v_{C} = \frac{2 \times 2 + 4}{3} = \frac{8}{3} \frac{m}{s} relative vel of B wrt CM v_{rel} = 4 - \frac{8}{3} = \frac{2}{3} ω \Rightarrow \frac{4}{3} = \frac{2}{3} ω ω = 2 \frac{rad}{s}$

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