A) \[\left[ {{M}^{0}}{{L}^{-1}}T \right]\]
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 :
\[y=A\sin (Bx+Ct+D)\] Each unit is dimensionless in bracket, then \[A=y=[L]\] \[B=1=[{{L}^{-1}}]\] \[C=\frac{1}{t}=[{{T}^{-1}}]\] D is dimensionless \[\therefore \] \[[ABCD]=[L][{{L}^{-1}}][{{T}^{-1}}]=[{{M}^{0}}{{L}^{0}}{{T}^{-1}}]\]
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