The surface of water in a water tank of cross section area 750 ,c… - Vidyadip

MCQ

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 $500\,mm ^2$ is $30\,cm / s$. At that instant, $\frac{d h}{d t}$ is $x \times 10^{-3} m / s$. The value of $x$ will be $.............$.

A
$3$
B
$4$
C
$6$
✓
$2$

✓

Answer

Correct option: D.

$2$

d
$A _1 V _1= A _2 V _2$

$750 \times 10^{-4} V _1=500 \times 10^{-6} \times 0.3$

$V _1=\frac{500 \times 3 \times 10^{-3}}{750}\,m / s$

$=2 \times 10^{-3}\,m / s$

$\frac{ dh }{ dt }=-2 \times 10^{-3}\,m / s$

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