A) The unit of\[ct\]is same as that of\[\lambda \]
B) The unit of\[x\]is same as that of \[\lambda \]
C) The unit of\[2\pi c/\lambda \] is same as that of\[2\pi x/\lambda t\]
D) The unit of\[c/\lambda \]is same as that of \[x/\lambda \]
Correct Answer: D
Solution :
Here,\[(2\pi ct/\lambda )\]as well\[(2\pi x/\lambda )\]are dimensionless. So, unit of\[ct\]is same as that of \[\lambda \]and unit of\[x\]is same as that of \[\lambda \] Since, \[\left[ \frac{2\pi ct}{\lambda } \right]=\left[ \frac{2\pi x}{\lambda } \right]=[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] \[\therefore \] \[\frac{2\pi c}{\lambda }=\frac{2\pi x}{\lambda t}\] In the option [d],\[\frac{x}{\lambda }\]is unit less. It is not the case with\[c/\lambda \].
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