Q129 / 160 · TS EAMCET 2005 · Physics

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 Figure

  • A
    1.5 rad/s
  • Correct answer
    B
    5.2 rad/s
  • C
    2.5 rad/s
  • D
    None of these

Solution

If rod is rotated about end $A$, then vertical component of velocity $v_{\perp}$ of end $A$ will be zero. $\begin{aligned} \therefore \quad \omega & =\frac{v \cos 60^{\circ}}{l}=\frac{\sqrt{3} v}{2 l} \\ & =\frac{\sqrt{3} \times 3}{2 \times 0.5}=5.2 \mathrm{rad} / \mathrm{s} \end{aligned}$

Hence, the correct answer is option: 'B'.

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