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A cylindrical vessel of height $500 \mathrm{~mm}$ has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it upto height $H$. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being 200 $\mathrm{mm}$. Find the fall in height (in $\mathrm{mm}$ ) of water level due to opening of the orifice.
[Take atmospheric pressure $=1.0 \times 10^5 \mathrm{Nm}^{-2}$, density of water $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ and $g=10$ $\mathrm{ms}^{-2}$. Neglect any effect of surface tension.]
[Take atmospheric pressure $=1.0 \times 10^5 \mathrm{Nm}^{-2}$, density of water $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ and $g=10$ $\mathrm{ms}^{-2}$. Neglect any effect of surface tension.]
Solution:
1712 Upvotes
Verified Answer
The correct answer is:
6
In this question we will have to assume that temperature of enclosed air about water is constant (or $p V=$ constant)
$$
\begin{gathered}
p=p_0-\rho g h \\
p_0[A(500-H)]=p[A(200)]
\end{gathered}
$$
Solving these two equations, we get
$$
\begin{aligned}
H & =206 \mathrm{~mm} \\
\therefore \quad \text { Level fall } & =(206-200) \mathrm{mm} \\
& =6 \mathrm{~mm}
\end{aligned}
$$
$$
\begin{gathered}
p=p_0-\rho g h \\
p_0[A(500-H)]=p[A(200)]
\end{gathered}
$$
Solving these two equations, we get
$$
\begin{aligned}
H & =206 \mathrm{~mm} \\
\therefore \quad \text { Level fall } & =(206-200) \mathrm{mm} \\
& =6 \mathrm{~mm}
\end{aligned}
$$
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