SATHEE: Properties of Matter 2 Question 23

Properties of Matter 2 Question 23

23. A column of mercury of length $10 c m$ is contained in the middle of a horizontal tube of length $1 m$ which is closed at both the ends. The two equal lengths contain air at standard atmospheric pressure of $0.76 m$ of mercury. The tube is now turned to vertical position. By what distance will the column of mercury be displaced? Assume temperature to be constant.

(1978)

momentum and, $25$ comes back with the same speed. The resultant pressure on the mesh will be (2019 Main, 11 Jan I)

(a) $ρ v^{2}$

(b) $\frac{1}{2} ρ v^{2}$

(d) $\frac{3}{4} ρ v^{2}$

5 Water flows into a large tank with flat bottom at the rate of $10^{- 4} m^{3} s^{- 1}$ . Water is also leaking out of a hole of area $1 c m^{2}$ at its bottom. If the height of the water in the tank remains steady, then this height is

(2019 Main, 10 Jan I)

(a) $4 c m$

(b) $2.9 c m$

(d) $1.7 c m$

6 The top of a water tank is open to air and its water level is maintained. It is giving out $0.74 m^{3}$ water per minute through a circular opening of $2 c m$ radius is its wall. The depth of the centre of the opening from the level of water in the tank is close to

(2019 Main, 9 Jan II)

(a) $4.8 m$

(b) $6.0 m$

(d) $9.6 m$

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Solution:

Let area of cross-section of the tube be $A$ .

(b)

Applying $p_{1} V_{1} = p_{2} V_{2}$ in $A$ and $B$ we have,

$\begin{aligned} p_{0} (45) (A) & = p_{1} (45 - x) A \\ or 76 \times 45 & = p_{1} (45 - x) \\ p_{0} (45) (A) & = p_{2} (45 + x) A \\ 76 \times 45 & = p_{2} (45 + x) \end{aligned}$