The surface of water in a water tank of cross-sectional area on the top of a house is m above the tap level. The speed of water coming out through the tap of cross-sectional area is . At that instant, is . The value of will be _______. [

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Solution

Q.
The surface of water in a water tank of cross-sectional 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-sectional 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 _______. [2023]

Ans.
(2)

$a_{1} v_{1} = a_{2} v_{2}$

$750 \times 10^{- 4} v_{1} = 500 \times 10^{- 6} \times 0.3$

$v_{1} = \frac{500 \times 3 \times 10^{- 3}}{750} m/s = 2 \times 10^{- 3} m/s$

$\Rightarrow \frac{d h}{d t} = - 2 \times 10^{- 3} m/s$

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