In the above problem the angular velocity of the system after the particle stick

Question

In the above problem the angular velocity of the system after the particle sticks to it will be

Options:

A . 0.3 rad/s

B . 5.3 rad/s

C . 10.3 rad/s

D . 89.3 rad/s

Answer: Option C
:
C
Initial angular momentum of bullet + initial angular momentum of cylinder
= Final angular momentum of (bullet + cylinder) system

\Rightarrow m v r + I_{1} ω = (I_{1} + I_{2}) ω^{'}

\Rightarrow m v r + I_{1} ω = (\frac{1}{2} M r^{2} + m r^{2}) ω^{'}

\Rightarrow 0.5 \times 5 \times 0.2 + 0.12 = (\frac{1}{2} 2 (0.2)^{2} + (0.5) (0.2)^{2}) ω^{'}

∴ ω^{'} = 10.3 r a d / s e c .

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