Question

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 ____

Answer 1

$A _1 V _1= A _2 V _2$
$750 \times 10^{-4} V _1=500 \times 10^{-6} \times 0.3$
$V _1=\frac{500 \times 3 \times 10^{-3}}{750} m / s$
$=2 \times 10^{-3} m / s$
$\frac{ dh }{ dt }=-2 \times 10^{-3} m / s$