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Q.

A small hole is made at the bottom of a hollow sphere. The water enters into it when it is taken to a depth of 40 cm under water. If the surface tension of water is 0.07 Nm^-1, diameter of the hole is

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a

10/7 mm

b

10/14 mm

c

2/15 m m

d

1/14 mm

answer is D.

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Detailed Solution

$\begin{array}{l} h = 40 cm, T = 0 .07 N / m \\ ∆ P = ρgh = \frac{2 T}{r} \Rightarrow r = \frac{2 T}{ρhg} = \frac{2 \times 0 .07}{10^{3} \times 9 .8 \times 40 \times 10^{- 2}} \\ \Rightarrow r = \frac{1}{2 \times 14} \times 10^{- 3} m = \frac{1}{2 \times 14} mm \\ \Rightarrow d = 2 r = \frac{1}{14} mm \end{array}$

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