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A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross-section ,A₁ and A₂, & velocities v₁ and v₂ respectively. The difference in the levels of the liquid in the two vertical tubes is h. Following observations are taken
(i) The volume of the liquid flowing through the tube in unit time A₁v₁
$(ii) v_{2} - v_{1} = \sqrt{2 g h}$
$(iii) v_{2}^{2} - v_{1}^{2} = 2 g h$
(iv) The energy per unit mass of the liquid is the same in both sections of the tube
The correct observations is/are

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(i) and (ii)

(i), (ii) and (iii)

(i), (iii) and (iv)

(i) and (iv)

answer is D.

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Detailed Solution

According to the equation of continuity, the volume of liquid flowing through the tube in unit time remains constant,
i.e., $A_{1} v_{1} = A_{2} v_{2}$ . Hence, option (a) is correct.

According to Bernoulli's theorem,

$P_{1} + \frac{1}{2} ρ v_{1}^{2} = P_{2} + \frac{1}{2} ρ v_{2}^{2}$

$\Rightarrow P_{1} - P_{2} = \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2}) \Rightarrow h ρ g = \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2})$

$∴ v_{2}^{2} - v_{1}^{2} = 2 g h$

Hence, option (c) is correct.
Also, according to Bernoulli's theorem. option (d) is correct.

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