| The position co-ordinates of a particle moving in a 3-D coordinate system is given by |
| \[~x=a\text{ }cos\omega t\] |
| \[y=a\text{ }sin\omega t\] and \[z=a\omega t\] |
| The speed of the particle is: [JEE Main 09-Jan-2019 Evening] |
A) \[a\omega \]
B) \[\sqrt{3}\,a\omega \]
C) \[\sqrt{2}\,a\omega \]
D) \[2\,a\omega \]
Correct Answer: C
Solution :
| [c] \[{{V}_{x}}=a\omega sin\omega t\] |
| \[{{V}_{y}}=a\omega cos\omega t\] |
| \[{{V}_{z}}=a\omega \] |
| \[\left| V \right|=\sqrt{V_{x}^{2}+V_{y}^{2}+V_{z}^{2}}\] |
| \[=\,\sqrt{{{a}^{2}}{{\omega }^{2}}\,{{\sin }^{2}}\,\omega t+{{a}^{2}}{{\omega }^{2}}\,{{\cos }^{2}}\,\omega t\,+{{a}^{2}}\,{{\omega }^{2}}}\] |
| \[\left| V \right|\,\,=\,\,\sqrt{2}\,a\omega \] |
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