Given below are two statements : Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation P_1-P_2=\rho g(~h_2-h_1) . Statement II : In ventury tube shown 2 gh=v_1^2-v_2^2 In the light of the above statements, choose the most appropriate answer from the options given below.

Statement I is correct but Statement II is incorrect.

Both Statement I and Statement II are correct.

Both Statement I and Statement II are incorrect.

Statement I is incorrect but Statement II is correct.

Properties of Matter PYQ — JEE Main 2024 · 4 Apr · Shift 1 · Q65 with Solution

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Correct answer: A

When the liquid is at rest, the fluid is in hydrostatic equilibrium. Then pressure variation with height is given by

$\frac{dP}{dz}=-\rho g$

If we take heights $h_1$ and $h_2$ measured upward from the same reference level, then integrating gives

$P_1-P_2=\rho g(h_2-h_1)$

So Statement I is correct.

For a venturimeter (or venturi tube), applying Bernoulli’s equation between points $1$ and $2$ :

= P_2+\frac{1}{2}\rho v_2^2+\rho gy_2$$ If the tube is horizontal, then $y_1=y_2$, so $$P_1-P_2=\frac{1}{2}\rho (v_2^2-v_1^2)$$ If the pressure difference is expressed in terms of height difference $h$ of the liquid column, then $$P_1-P_2=\rho g h$$ Therefore, $$\rho g h=\frac{1}{2}\rho (v_2^2-v_1^2)$$ $$2gh=v_2^2-v_1^2$$ But the statement given is $$2gh=v_1^2-v_2^2$$ which has the **wrong sign**. Hence **Statement II is incorrect**. --- 3. **Conclusion** - Statement I: Correct - Statement II: Incorrect Therefore, the correct option is: $$\boxed{\text{A}}$$