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JEE Main 20231 FebruaryEvening Shift
Exam
JEE Main
Year
2023
Date
1 February
Shift
Evening Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2023 · 1 February · Evening Shift · Physics · Mechanical Properties of Fluids

The surface of water in a water tank of cross section area 750 cm ^...

The surface of water in a water tank of cross section area 750cm2750{cm}^{2} on the top of a house is hmhm. above the tap level. The speed of water coming out through the tap of cross section area 500mm2500{mm}^{2} is 30cms−130cm{s}^{- 1}. At that instant, dhdt\dfrac{dh}{dt} is x×10−3ms−1x \times {10}^{- 3}m{s}^{- 1}. The value of xx will be ______.

Correct answer

0

Step-by-step solution

Using continuity equation

A1v1=A2v2{A}_{1}{v}_{1} = {A}_{2}{v}_{2}

We have,

750×10−4v1=500×10−6×0.3750 \times {10}^{- 4}{v}_{1} = 500 \times {10}^{- 6} \times 0 . 3

v1=500×3×10−3750{v}_{1} = \dfrac{500 \times 3 \times {10}^{- 3}}{750}

=2×10−3ms−1= 2 \times {10}^{- 3}m{s}^{- 1}

Thus, dhdt=−2×10−3ms−1\dfrac{dh}{dt} = - 2 \times {10}^{- 3}m{s}^{- 1}

Hence, the value of x=2x = 2.

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