Verified Solution • 2025–26 Session moderate

QJEEM23Ph344b: JEE Main 2023 Physics - Class 11 JEEM23Ph344b Solution: The surface of water in a water tank of cross section area on…

The surface of water in a water tank of cross section area 750 cm2750 \mathrm{~cm}^{2} on the top of a house is h mh \mathrm{~m} above the tap level. The speed of water coming out through the tap of cross section area 500 mm2500 \mathrm{~mm}^{2} is 30 cm/s30 \mathrm{~cm} / \mathrm{s} . At that instant, dhdt\frac{d h}{d t} is x×10−3 m/sx \times 10^{-3} \mathrm{~m} / \mathrm{s} . The value of xx will be ____________.

Step-by-Step Verified Solution

amp;AV=avamp;750×10−4×(dhdt)=(500×10−6)(30×10−2)amp;dhdt=15×10−575×10−3amp;=15×10−2amp;=2×10−3 m/samp;∴x=2\begin{aligned} & \mathrm{AV}=\mathrm{av} \\\\ & 750 \times 10^{-4} \times\left(\frac{d h}{d t}\right)=\left(500 \times 10^{-6}\right)\left(30 \times 10^{-2}\right) \\\\ & \frac{d h}{d t}=\frac{15 \times 10^{-5}}{75 \times 10^{-3}} \\\\ & =\frac{1}{5} \times 10^{-2} \\\\ & =2 \times 10^{-3} \mathrm{~m} / \mathrm{s} \\\\ & \therefore x=2\end{aligned}

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