Question

Two points $A$ and $B$ on a disc have velocities $v_1$ and $v_2$ at some moment. Their directions make angles ${60}^o$ and ${30}^o$ respectively with the line of separation as shown in figure. The angular velocity of disc is not given by :

• A. $\frac{v_1}{\sqrt{3}d}$
• B. $\frac{v_2}{d}$
• C. $\left(\frac{\sqrt{3}{v}_1-v_2}{2d}\right)$
• D. None of these

Answer 1

The correct option is D None of these

For rigid body separation between two point remains same.
$v_{1}cos{60}^0=v_{2}cos{30}^0$
$\frac{v_1}{2}=\frac{\sqrt{3}{v}_2}{2}\Rightarrow v_1=\sqrt{3}{v}_2$
${\omega }_{dsc}=|\frac{v_{1}sin{60}^0-v_{2}sin{30}^0}{d}|$
$=\left(\frac{\sqrt{3}{v}_1-v_2}{2d}\right)$
$=|\frac{\sqrt{3}\times \sqrt{3}{v}_2-v_2}{2d}|=\frac{2v_2}{2d}=\frac{v_2}{d}$

$\Rightarrow {\omega }_{dsc}=\frac{v_2}{d}=\frac{v_1}{\sqrt{3}d}$

All the options are correct.