First slide

Surface tension and surface energy

Question

A hollow sphere has a small hole in it. On lowering the sphere in a tank of water, it is observed that water enters into the hollow sphere at a depth of 40 cm below the surface. Surface tension of water is 7 x 10^-2 N/m. The diameter of the hole is

Moderate

A

$\frac{1}{28} mm$
B

$\frac{1}{21} mm$
C

$\frac{1}{14} mm$
D

$\frac{1}{7} mm$

Solution

On lowering the sphere into water with hole, excess pressure supports the water up to some height till which no leakage takes place.

$\begin{array}{l} \Rightarrow \frac{2 T}{R} = h ρ g \\ \Rightarrow \frac{40}{100} \times 1000 \times 9.8 = \frac{2 \times 7 \times 10^{- 2}}{R} \\ ⇒ R = \frac{14 \times 10^{- 2} \times 100}{40 \times 1000 \times 9.8} m = \frac{14 \times 1000}{40 \times 1000 \times 9.8} mm \\ = \frac{1}{28} mm \\ Diameter = 2 R = \frac{1}{14} mm \end{array}$

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