A) \[\frac{\sqrt{3}{{v}_{1}}}{d}\]
B) \[\frac{{{v}_{2}}}{\sqrt{3}d}\]
C) \[\frac{{{v}_{2}}-{{v}_{1}}}{d}\]
D) \[\frac{{{v}_{2}}}{d}\]
Correct Answer: D
Solution :
[D]For rigid body body separation between two point remains same. |
\[{{v}_{1}}\cos 60{}^\circ ={{v}_{2}}\cos 30{}^\circ \] |
\[\frac{{{v}_{1}}}{2}=\frac{\sqrt{3}{{v}_{2}}}{2}\Rightarrow {{v}_{1}}=\sqrt{3}\,\,{{v}_{2}}\] |
\[{{\omega }_{disc}}=\left| \frac{{{v}_{2}}\sin 30{}^\circ -{{v}_{1}}\sin 60{}^\circ }{d} \right|=\left| \frac{\frac{{{v}_{2}}}{2}-\frac{\sqrt{3}{{v}_{1}}}{2}}{d} \right|\] |
\[=\left| \frac{{{v}_{2}}-\sqrt{3}\times \sqrt{3}{{v}_{2}}}{2d} \right|=\frac{2{{v}_{1}}}{2d}=\frac{{{v}_{2}}}{d}\] |
\[{{\omega }_{disc}}=\frac{{{v}_{2}}}{d}\] |
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