Question

If the value of surface tension of a liquid is $70\text{ dyne/cm}$, then its value in $\text{N/m}$ will be.
$\begin{align}
  & \text{A)7}\times {{10}^{3}}\text{N/m} \\
 & \text{B)7}\times {{10}^{2}}\text{N/m} \\
 & \text{C)7}\times {{10}^{-2}}\text{N/m} \\
 & \text{D)70N/m} \\
\end{align}$

Answer 1

Hint: Dyne is a unit of force and is smaller than the unit Newton. Centimetre is a unit of length and also smaller than the unit metre. Students can also take the unitary approach to take forward this particular conversion.

Complete step-by-step answer:
Let us first of all look into the physical meaning of surface tension, in order to learn about its units.
Definition-
Surface tension of a liquid can be defined as the force applied per unit length in a direction perpendicular to the surface of the liquid. The SI unit of force is Newton and the Si unit of length is metre and as such the Si unit of surface tension is Newton per metre, mathematically represented as $\text{N/m}$ .
In the question we are given the value of the surface tension of a liquid in terms of $\text{dyne/cm}$, which is in the CGS system and we are asked to convert the value to the SI system. Let us use the unitary method to do the same.
We know that,
$\begin{align}
  & \text{1 Newton(N) = 1}{{\text{0}}^{5}}\text{dynes} \\
 & \Rightarrow \text{1 dyne = }\dfrac{1}{{{10}^{5}}}\text{N} \\
 & \Rightarrow \text{1 dyne = 1}{{\text{0}}^{-5}}\text{N} \\
\end{align}$
In the above calculations we have determined the value of $\text{1 dyne}$, so now we can easily calculate its value for $70\text{ dyne/cm}$( because we already know that $\text{1 cm = 1}{{\text{0}}^{-2}}\text{ m}$).
$\begin{align}
  & \text{1 dyne = 1}{{\text{0}}^{-5}}\text{N} \\
 & \Rightarrow \text{70 dyne = 7}\times \text{1}{{\text{0}}^{-4}}\text{N} \\
 & \text{Also,} \\
 & \text{1 cm = 1}{{\text{0}}^{-2}}\text{m} \\
 & \Rightarrow \text{70dyne/cm = 7}\times \text{1}{{\text{0}}^{-2}}\text{N/m} \\
\end{align}$
Therefore by the above calculations, it is clear that the answer to the given question is option $\text{C)7}\times {{10}^{-2}}\text{N/m}$.

Note: Students must be very careful while carrying out the calculations as they may find really confusing as to which is the greater unit. In that case they need to remember that, in SI units, mostly the units are greater than the units considered in the CGS system.