Question

There is a small hole in a hollow sphere. The water enters into it when it is taken to a depth of $40\text{cm}$ under water. The surface tension of water is $0.07\text{N/m}$. The diameter of the hole is
[Take $g=10{\text{m/s}}^2$]

• A. $7\text{mm}$
• B. $0.07\text{mm}$
• C. $0.007\text{mm}$
• D. $0.7\text{mm}$

Answer 1

The correct option is B $0.07\text{mm}$

Given,
Depth of water at which hollow sphere is taken, $h=40\text{cm}=0.4\text{m}$
Surface Tension of water, $T=0.07\text{N/m}$
To find : Diameter of hole, $d=?$
Excess pressure of the hole is given by
$\Delta P=\frac{4T}{d}$
$[$ one side of hole is air and on other side is water $]$
$=\frac{4\times 0.07}{d}=\frac{0.28}{d}$ .......(1)
Pressure due to height of water,
$P=\rho gh$
$=1000\times 10\times 0.4$
$=4000{\text{N/m}}^2$ ..........(2)
Water will enter into the hollow sphere if excess pressure will be equal to or lesser than the pressure due to height of water.
From (1) and (2)
$\frac{0.28}{d}=4000$
$\Rightarrow d=7\times {10}^{-5}\text{m}=0.07\text{mm}$