Question

The surface tension of a liquid in a CGS system is 45\[dyne/cm\]. Its value in SI system is:

(A) $4.5N{m^{ - 1}}$

(B) $0.045N{m^{ - 1}}$

(C) $0.0045N{m^{ - 1}}$

(D) $0.45N{m^{ - 1}}$

Answer 1

Hint: The surface tension can be converted into the SI unit system by converting dyne into newton and centimeter into meter\[{\text{ }}1{\text{ }}dyne/cm{\text{ }} = {\text{ }}{10^{ - 3}}N/m\]. Multiply the conversion value to the surface tension to get it in terms of SI units.

Complete step-by-step solution

The SI unit of force is Newton (N) and the CGS unit of force is dyne.

$1dyne = {10^{ - 5}}N$

The SI unit of length is meter (m) and the CGS unit is centimeter(cm).

$1cm = {10^{ - 2}}m$

So, dyne per centimeter (\[dyne/cm\]) can be written in terms of newton per meter (\[N/m\])

$\dfrac{{dyne}}{{cm}} = \dfrac{{{{10}^{ - 5}}}}{{{{10}^{ - 2}}}} = {10^{ - 3}}N/m$

Therefore, \[{\text{ }}1{\text{ }}dyne/cm{\text{ }} = {\text{ }}{10^{ - 3}}N/m\]

For 45 \[dyne/cm\]in terms of \[N/m\] is given by multiplying the value

$
  45 \times {10^{ - 3}} \\

   = 0.045N/m \\

 $
Hence the surface tension of a liquid in SI system is $0.045N{m^{ - 1}}$

the correct option is B.

Note: Surface tension can be defined as the property which resists an external force due to the cohesive nature of molecules. The surface tension of a liquid in an FPS system is poundal per foot (pdl/ft). Millinewton per meter and pound per inch are some other units of surface tension.