A) \[\left[ {{M}^{0}}{{L}^{-1}}{{T}^{0}} \right]\]
B) \[\left[ {{M}^{0}}{{L}^{0}}{{T}^{-1}} \right]\]
C) \[\left[ {{M}^{0}}{{L}^{-1}}{{T}^{-1}} \right]\]
D) \[\left[ {{M}^{0}}{{L}^{0}}{{T}^{0}} \right]\]
Correct Answer: B
Solution :
\[y=A\sin (Bx+Ct+D)\] As each term inside the bracket is dimensionless, so \[A=y=[{{L}^{1}}]\] \[B=\frac{1}{x}=[{{L}^{-1}}]\] \[C=\frac{1}{t}=[{{T}^{-1}}]\] and D is dimensionless. \[\therefore \] \[[ABCD]=[L][{{L}^{-1}}][{{T}^{-1}}][1]\] \[=[{{M}^{0}}{{L}^{0}}{{T}^{-1}}]\]
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