The volume V of water passing through a point of a uniform tube during t seconds is related to the cross-sectional area A of the tube and velocity u of water by the relation.
$V \propto A^\alpha u^\beta t^\gamma$
Which one of the following will be true?
Answer & explanation
Correct answer: option 2
$V = k . \Delta^\alpha u^{\beta} t^{\gamma}$
$L^3=k\left(L^2\right)^\alpha . \left(L T^{-1}\right)^\beta . (T)^\gamma$
$L^3=k . L^{(2\alpha+\beta)} T^{-\beta+\gamma}$
$2 \alpha+\beta=3$
$-\beta+\gamma=0$
$\beta=\gamma,~~2\alpha+\beta=3$
so are can conclude that
$\alpha ≠ \beta=\gamma$