Question

A rigid horizontal smooth $\mathrm{rod}AB$ of mass $0.75kg$ and length $40cm$ can rotate freely about a fixed vertical axis through its midpoint $O$. Two rings each of mass $1kg$ initially at rest are placed at a distance of $10cm$ from $O$ on either side of the rod. The rod is set in rotation with an angular velocity of $30$ radian per sec and when the rings reach the ends of the rod, the angular velocity in rad/sec is

• A. 5
• B. 10
• C. 15
• D. 20

Answer 1

Answer: (B)

According to the conservation of angular momentum
$I_1{\omega }_1=I_2{\omega }_2$
$\therefore \left[\frac{M{L}^2}{12}+2m{r}^2\right]{\omega }_1=\left[\frac{M{L}^2}{12}+2m{\left(\frac{L}{2}\right)}^2\right]{\omega }_2$
or $\left[\frac{0.75\times (0.4{)}^2}{12}+2\times 1\times (0.1{)}^2\right]\times 30$
$=\left[\frac{0.75\times (0.4{)}^2}{12}+2\times 1\times (0.2{)}^2\right]\times {\omega }_2$
or ${\omega }_2=\frac{(0.01+0.02)30}{(0.01+0.08)}=\frac{0.03\times 30}{0.09}=10rad/sec$