SATHEE: Properties of Matter 3 Question 2

Properties of Matter 3 Question 2

8. Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $ρ$ , the surface tension of water is $T$ and the atmospheric pressure is $p_{0}$ . Consider a vertical section $A B C D$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

(a) $| 2 p_{0} R h + π R^{2} ρ g h - 2 R T |$

(2007, 3M)

(b) $| 2 p_{0} R h + R ρ g h^{2} - 2 R T |$

(c) $| p_{0} π R^{2} + R ρ g h^{2} - 2 R T |$

(d) $| p_{0} π R^{2} + R ρ g h^{2} + 2 R T |$

Objective Questions II (Only one correct option)

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Answer:

Correct Answer: 8. (a)

Solution:

Velocity of efflux at a depth $h$ is given by $v = \sqrt{2 g h}$ . Volume of water flowing out per second from both the holes are equal.

$\begin{aligned} ∴ a_{1} v_{1} = a_{2} v_{2} \\ or \\ (L^{2}) \sqrt{2 g (y)} = π R^{2} \sqrt{2 g (4 y)} or R = \frac{L}{\sqrt{2 π}} \end{aligned}$

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