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?


ANSWER

$$a \ne \beta = \gamma $$


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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