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There is a small hole near the botttom of an open tank filled with a liquid.The speed of water ejected does not depend on

$\begin{array}{1 1}(A)\;\text{Perimeter of the hole}\\(B)\;\text{Density of the liquid}\\(C)\;\text{Height of the liquid from the hole}\\(D)\;\text{Acceleration due to gravity}\end{array} $

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Applying Bernoulli's theorem to A & B
$\rho_A+\large\frac{1}{2}$$\rho V_A^2+\rho gh=\rho_B+\large\frac{1}{2}$$\rho V_B^2$
$\rho_o+\large\frac{1}{2}$$\rho V_A^2+\rho gh=\rho_o+\large\frac{1}{2}$$\rho V_B^2$
$\large\frac{1}{2}$$\rho V_A^2+\rho g h=\large\frac{1}{2}$$\rho V_B^2$------(1)
$A_AV_A=A_BV_B$
$\pi R^2V_A=A_BV_B$
$V_A=\large\frac{r^2}{R^2}$$V_B$----(2)
From (1) & (2)
$\large\frac{1}{2}$$\rho (\large\frac{r^2}{R^2}$$V_B)^2+\rho gh=\large\frac{\rho}{2}$$V_B^2$
$\large\frac{\rho}{2}$$V_B^2-\large\frac{1}{2}$$\rho (\large\frac{r^2}{R^2}$$V_B)^2=\rho gh$
Hence depending on f,r,R,h & g$
Hence (B) is the correct answer.
answered May 9, 2014 by sreemathi.v
 

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