The instantaneous velocity of a point $B$ of the given rod of length $0.5 \mathrm{~m}$ is $3 \mathrm{~m} /…
The instantaneous velocity of a point $B$ of the given rod of length $0.5 \mathrm{~m}$ is $3 \mathrm{~m} / \mathrm{s}$ in the represented direction. The angular velocity of the rod for minimum velocity of end $A$ is
1.5 rad/s
5.2 rad/s
2.5 rad/s
None of these
Solution
If rod is rotated about end $A$, then vertical component of velocity $v_{\perp}$ of end $A$ will be zero.
$\begin{aligned}
\therefore \quad \omega & =\frac{v \cos 60^{\circ}}{l}=\frac{\sqrt{3} v}{2 l} \\
& =\frac{\sqrt{3} \times 3}{2 \times 0.5}=5.2 \mathrm{rad} / \mathrm{s}
\end{aligned}$
