Question

A long slender rod of mass $2kg$ and length $4m$ is placed on a smooth horizontal table. Two particles of masses $2kg$ and $1kg$ strike the rod simultaneously and stick to the rod after collision as shown in Figure.
Angular velocity of the rod after collision is

• A. $11/17rad/s$
• B. $rad/s$
• C. $19/17rad/s$
• D. $30/17rad/s$

Answer 1

Answer: (D)

$30/17rad/s$

By conservation of angular momentum

$2\times 10\times 1-1\times 10\times 1=I\omega$

$10=I\omega$

$I=\frac{M{L}^2}{12}+m_1{r}_1^2+m_2{r}_2^2$

$=\frac{2\times 16}{12}+3$

$I=\frac{8+9}{3}=\frac{17}{3}$

$10=I\omega$

$\omega =\frac{10}{I}=\frac{10}{17/3}\Rightarrow \frac{30}{17}rad/sec$