Question

Prove that, equivalent S.I. unit of surface
tension is J/m2.​

Answer 1

Given,

A quantity parameter = surface tension

To prove,

The equivalent S.I. unit of surface

tension is J/m2.

Solution,

We can simply solve this numerical problem by using the following process:

Mathematically,

Surface tension is defined as the tendency of a liquid surface at rest to shrink into a minimum surface area possible. It is represented as the force acting per unit length.

Surface tension = force/length

{Equation-1}

Also, work done = force × length

{Equation-2}

And, the SI unit of force = Newtons (N)

SI unit of length = meters (m)

SI unit of work done = N×m = Joules (J)

{Statement-1}

Now, according to the question;

LHS = Surface tension

= force/length

{according to equation-1}

= (force×length)/(length×length)

= (work done)/(length)^2

{according to equation-2}

= (SI unit in Joules)/(SI unit in meters)^2

{according to statement-1}

= Joule/(meter)^2 = J/m^2 = RHS

Hence, it is proved that the equivalent S.I. unit of surface tension is J/m2.

Answer 2

Answer:

The SI unit of surface tension  $=\frac{\mathrm{J}}{\mathrm{m}^{2}}$

Explanation:

• Surface tension is a feature of any liquid that seeks to keep its free surface area as small as possible.
• The force operating per length on an imaginary line drawn tangentially on the free surface of a liquid is known as surface tension.

Surface tension S = Force/Length = F/l = Work done/Change in area.

The SI unit of surface tension = $\frac{\text { newton }(\mathrm{N})}{\text { metre }(\mathrm{m})}=\frac{\mathrm{N}}{\mathrm{m}} \cdot \frac{\mathrm{m}}{\mathrm{m}}=\frac{\mathrm{J}}{\mathrm{m}^{2}}$