Which of the following relations cannot be de | vedclass

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(D) Dimensional analysis is a powerful tool for checking the consistency of equations,but it has significant limitations. $1$. It cannot derive equati

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$y=A\sin(\omega t+kx)$

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(D) Dimensional analysis is a powerful tool for checking the consistency of equations,but it has significant limitations. $1$. It cannot derive equations involving trigonometric,exponential,or logarithmic functions because these functions are dimensionless. $2$. It cannot determine dimensionless constants (like $1/2$ or $\pi$) in a formula. $3$. It cannot derive equations containing more than three physical quantities if they are independent. In the given options: - $v=u+at$ is a linear relation that can be checked for dimensional consistency. - $k=\frac{1}{2}mv^2$ is a relation where the constant $1/2$ cannot be determined,but the dimensions can be checked. - $y=A\sin(\omega t+kx)$ involves a trigonometric function. Dimensional analysis cannot be used to derive or verify the structure of such transcendental equations because the argument of the sine function must be dimensionless,and the function itself does not have a simple power-law form. Therefore,the relation $y=A\sin(\omega t+kx)$ cannot be deduced using dimensional analysis.

Which of the following relations cannot be deduced using dimensional analysis? [the symbols have their usual meanings]

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