Question

If the force required to pull out a glass plate of length 9.8cm and thickness 2mm from a liquid is 0.6gm−wt. The surface tension of water is $N{m^{ - 1}}$:
A.2.94 $\times$ ${10^{ - 3}}$
B.29.4 $\times$ ${10^3}$
C.29.4 $\times$ ${10^{ - 2}}$
D.29.4 $\times$ ${10^{ - 3}}$

Answer 1

Hint: Surface tension means having ability to resist the liquid. When the force is applied on the glass plate from the liquid which is having some weight then we need to calculate the surface tension of water by using the concern formula.

Complete step by step solution:
From the given data:
$l$=9.8cm
t=2mm
F=0.6gmwt
Surface tension=?
The surface tension of the water is calculated as
 $\sigma = \dfrac{F}{{2(l + t)}}$
Convert the gram weight into newton kg
$\sigma = \dfrac{{0.6 \times {{10}^{ - 3}} \times 9.8}}{{2(9.8 \times {{10}^{ - 2}} + 2 \times {{10}^{ - 3}})}}$
$\
 \implies \sigma = \dfrac{{0.6 \times {{10}^{ - 3}} \times 9.8}}{{2(0.1)}} \\
\implies \sigma = 29.4 \times {10^{ - 3}}N{m^{ - 1}} \\
\ $

So, the correct answer is “Option D”.

Additional Information:
We can explain surface tension with an example of when the water droplets form on the surface of the table because the droplets at the surface group together opposite to the force of gravity.
Cohesive forces that exist in between the molecules of the liquid without any chemical bonding which give rise surface tension. When the forces exist between like or similar molecules are called cohesive forces. When the forces exist between molecules they are called adhesive forces.

Note:
When we are going to solve this kind of numerical, students should be very careful about the conversion from gram weight into newton kg by taking the appropriate values and also we should be aware of the conversion of the CGS system to SI unit.
Surface tension is usually referred to as the ability of resisting the liquid from the force of gravity.