Question

A rigid horizontal smooth rod AB of mass 0.75 Kg and length 40 cm can rotate freely about a fix verticle axis through its midpoint O.Two rings each of mass 1 kg initially at rest at a distance of 10 cm from O on either side of the rod. The rod is set in rotation with an angular velocity of 30 radians per second 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

The correct option is B 10

$\begin{array}{c}{I}_1{w}_1=I_2{w}_2\\ \Rightarrow \left[\frac{M{L}^2}{12}+m{\left(\frac{10}{100}\right)}^2\times 2\right]30=\left[\frac{M{L}^2}{12}+m{\left(\frac{20}{100}\right)}^2\times 2\right]w_2\\ \Rightarrow \left[\frac{0.75}{12}+\times \frac{40}{100}\times \frac{40}{100}+\frac{1\times 100}{10000}\times 2\right]30=\left[\frac{0.75}{12}\times \frac{40}{100}\times \frac{40}{100}\times 2\right]w_2\\ \Rightarrow w=10\end{array}$

$\therefore$ Option $B$ is correct.