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(C) The statement is correct. Dimensional analysis relies on the principle of homogeneity of dimensions,which allows us to equate powers of fundamenta

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(C) The statement is correct. Dimensional analysis relies on the principle of homogeneity of dimensions,which allows us to equate powers of fundamental quantities $(M, L, T)$ to solve for unknown exponents. If a physical quantity $X$ depends on three quantities $a, b,$ and $c$,where $a$ and $b$ have the same dimensions,the relationship would be of the form $X = k \cdot a^x \cdot b^y \cdot c^z$. Since $a$ and $b$ have the same dimensions,say $[M^p L^q T^r]$,the expression becomes $X = k \cdot ([M^p L^q T^r])^x \cdot ([M^p L^q T^r])^y \cdot c^z = k \cdot ([M^p L^q T^r])^{x+y} \cdot c^z$. Here,we can only determine the value of $(x+y)$ and $z$ through dimensional analysis,but we cannot individually determine the values of $x$ and $y$. Therefore,the unique formula cannot be derived using this method.

Even if a physical quantity depends upon three quantities,out of which two are dimensionally same,then the formula cannot be derived by the method of dimensions. This statement

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