The volume V of a liquid crossing through a tube is related to the area of cross-section A, velocity v and times t as $V \propto A^{a} V^{b} t^{c}$ which of the following is correct

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$a \neq b \neq c$

$a = b = c$

$a \neq b = c$

$a = b \neq c$

answer is C.

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Detailed Solution

$\begin{array}{l} {VαA}^{a} v^{b} t^{c} \Rightarrow L^{3} α {(L^{2})}^{a} {({LT}^{- 1})}^{b} (T)^{c} \\ 2 a + b = 3 \Rightarrow - b + c = 0 \Rightarrow b = c \\ ∴ a \neq b = c \end{array}$

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