Question

Two beads, each of mass ‘m’ slide from rest from the position shown along a smooth massless rod of length 2L. The rod is initially rotated with an angular velocity of $\sqrt{\frac{g}{L}}$ about the vertical axis. The speed of each bead at the time of leaving the rod is

• A. $\sqrt{\frac{g}{2L}}$
• B. $\sqrt{2gL}$
• C. $\sqrt{gL}$
• D. $\frac{\sqrt{gL}}{4}$

Answer 1

The correct option is D

$\frac{\sqrt{gL}}{4}$

Applying the principle of conservation of angular momentum about the center

$2m\frac{L^2}{4}\sqrt{\frac{g}{L}}=2m{L}^2{\omega }^1$ and $v=L{\omega }^1=\frac{\sqrt{gL}}{4}$