JEE MAIN - Physics (2024 - 4th April Morning Shift - No. 5)
Given below are two statements :
Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $$\mathrm{P}_1-\mathrm{P}_2=\rho g\left(\mathrm{~h}_2-\mathrm{h}_1\right)$$.
Statement II : In ventury tube shown $$2 \mathrm{gh}=v_1^2-v_2^2$$
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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.
Explanation
If speed $$=0$$
Then $$P_1+\rho g h_1=P_2+\rho g h_2$$
In given ventury tube,
$$\begin{aligned} & \qquad P_1+\rho g h+\frac{1}{2} \rho v_1^2=P_2+\frac{1}{2} \rho v_2^2 \\ & \Rightarrow \frac{1}{2} \rho\left(v_1^2-v_2^2\right)=\left(P_2-P_1\right)-\rho g h \\ & \Rightarrow v_1^2-v_2^2=\frac{2\left(P_2-P_1\right)}{\rho}-2 g h \end{aligned}$$
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