JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Fluid Mechanics

The surface of water in a water tank of cross section area

750 cm^{2}

on the top of a house is

h m

. above the tap level. The speed of water coming out through the tap of cross section area

500 mm^{2}

30 cm / s

. At that instant,

\frac{d h}{d t}

x \times 1 0^{- 3} m / s

. The value of

x

will be ____.

Answer: 2

Solution

The water leaving the tap and the fall of the surface are linked by continuity,

A_{1} \frac{d h}{d t} = A_{2} v

. With

A_{1} = 750 \times 1 0^{- 4} m^{2}

A_{2} = 500 \times 1 0^{- 6} m^{2}

and

v = 0.30 m s^{- 1}

\frac{d h}{d t} = \frac{( 500 \times 1 0 ^{- 6} ) ( 0.30 )}{750 \times 1 0 ^{- 4}} = 2 \times 1 0^{- 3} m s^{- 1}

. The surface falls at

2 \times 1 0^{- 3}

m/s, so

x = 2

JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Integer answer

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