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 \[2\pi \times /\lambda t\]
D) The unit of \[c/\lambda \] is same as that of\[x/\lambda \].
Correct Answer: C
Solution :
Here, \[(V-20)=-\frac{2}{3}\,(S-0)\] as well as \[\Rightarrow \] are dimensionless. So, unit of ct is same as that of \[\lambda \]. Unit of \[v=20-\frac{2}{3}\,S\] is same as that of \[S=15\] Since, \[{{\left. v=\frac{ds}{dt} \right|}_{S=15\,m}}{{\left. =-\frac{2}{3}\,\frac{dS}{dt} \right|}_{S=15\,m}}=-\frac{20}{3}\,m{{s}^{-2}}\] Hence. \[=\frac{dv}{dt}=-\frac{2}{3}\,\frac{dS}{dt}\] In the option [d], \[\therefore \] is unit less. It is not the case with\[{{\left. \frac{dV}{dt} \right|}_{S=15\,m}}{{\left. =-\frac{2}{3}\frac{dS}{dt} \right|}_{S=15\,m}}=-\frac{20}{3}\,m{{s}^{-2}}\].
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