Question

The volume $V$ of water flowing with velocity $v$ through any cross-section of area $A$ of a uniform tube in interval $t$ is given by the equation $V \propto A^{\alpha}v^{\beta}t^{\gamma}$. Here $\alpha$, $\beta$ and $\gamma$ are constants. Which one of the following statements is correct?

• A. $\alpha= \beta= \gamma$
• B. $\alpha\ne \beta= \gamma$
• C. $\alpha= \beta\ne \gamma$
• D. $\alpha\ne \beta\ne \gamma$

Answer 1

Answer: (A)

In $t$ time, water flows a distance $vt$ of the tube of cross sectional area $A$. Therefore, volume of water flowing through the cross-section is $Avt$.
$\Rightarrow \alpha= \beta= \gamma=1$