The instantaneous velocity of point $\mathrm{B}$ of the given rod of length $0.5 \mathrm{m}$ is $3 \mathrm{m} {\mathrm{s}}^{-1}$ in the represented direction. What is the angular velocity (in $\mathrm{rad} {\mathrm{s}}^{-1}$) of the rod for the minimum possible magnitude of the velocity of the end $\mathrm{A}$?  

Solution

If rod is rotated about end A, then vertical component of velocity, ${\mathrm{v}}_{\perp }$ of end a will be zero.



$\therefore \mathrm{\omega }=\frac{\mathrm{v}{\sin 60}^{\mathrm{o}}}{\mathrm{l}}=\frac{\sqrt{3}\mathrm{ }\mathrm{v}}{2\mathrm{l}}$

$=\frac{\sqrt{3}\times 3}{2\times 0.5}=5.2$ $\mathrm{rad} {\mathrm{s}}^{-1}$

Hence, the correct answer is 5.2.