Physics

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?

$a \ne \beta = \gamma$

SOLUTION
The relation is given by

$V\propto A^{\alpha}u^{\beta}t^{\gamma}$

$[M^0L^3T^0]=[L^{2\alpha}L^{\beta}T^{-\beta}T^{\gamma}]$

By equating the coefficient,

$\gamma-\beta=0$

$\gamma=\beta$. . . . . .(1)

and $2\alpha+\beta =3$

The correct option is B.

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Single Correct Medium Published on 18th 08, 2020
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