Question

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

• A. 0.3 rad/s
• B. 5.3 rad/s
• C. 10.3 rad/s
• D. 89.3 rad/s

Answer 1

The correct option is C 10.3 rad/s

Initial angular momentum of bullet + initial angular momentum of cylinder
= Final angular momentum of (bullet + cylinder) system
$\Rightarrow mvr+I_1\omega =(I_1+I_2){\omega }^{\prime }$
$\Rightarrow mvr+I_1\omega =(\frac{1}{2}M{r}^2+m{r}^2){\omega }^{\prime }$
$\Rightarrow 0.5\times 5\times 0.2+0.12=\left(\frac{1}{2}2\right(0.2{)}^2+\left(0.5\right)\left(0.2{)}^2\right){\omega }^{\prime }$
$\therefore {\omega }^{\prime }=10.3rad/sec.$