Two points of a rod move with velocities 3 v & v perpendicular to the rod and in the same direction, separated by a distance 'r'. The angular velocity of rod is :

Answers (1)

                 

\begin{aligned} &\text { Let w be the angular velocity of the rod about point } 0 \text { . }\\ &\text { For } \mathrm{A}: 3 \mathrm{v}=(\mathrm{r}+\mathrm{x}) \mathrm{w}\\ &\text { For } \mathrm{B} : \mathrm{v}=\mathrm{xw}\\ &\text { On Subtracting we get, } 3 \mathrm{v}-\mathrm{v}=(\mathrm{r}+\mathrm{x}) \mathrm{w}-\mathrm{xw}\\ &\Longrightarrow 2 \mathrm{v}=\mathrm{rw} \\ &\Longrightarrow \frac{2 \mathrm{v}}{r}=\mathrm{w} \end{aligned}

 

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