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 Aαvβtγ. Here α, β and γ are constants. Which one of the following statements is correct?

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 Aαvβt&gamma;. Here α, β and &gamma; are constants. Which one of the following statements is correct? (A) α= β= &gamma; (B) α≠ β= &gamma; (C) α= β≠ &gamma; (D) α≠ β≠ &gamma;

Tardigrade Admin · Accepted Answer

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. ⇒ α= β= &gamma;=1

Q. 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 $V \propto A^{α} v^{β} t^{γ}$ . Here $α$ , $β$ and $γ$ are constants. Which one of the following statements is correct?

$α = β = γ$

$α \neq = β = γ$

$α = β \neq = γ$

$α \neq = β \neq = γ$

In $t$ time, water flows a distance $v t$ of the tube of cross sectional area $A$ . Therefore, volume of water flowing through the cross-section is $A v t$ .
$\Rightarrow α = β = γ = 1$

Q. 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∝Aαvβtγ. Here α, β and γ are constants. Which one of the following statements is correct?

α=β=γ

α=β=γ

α=β=γ

α=β=γ