Question

The surface tension is $T = \dfrac{F}{l}$ , then the dimensions of surface tension is:
A $ML{T^{ - 2}}$
B $M{T^{ - 2}}$
C ${M^0}{L^0}{T^0}$
D None of these

Answer 1

Dimensional formula is representation of a formula in dimensional form, at first we take the coefficient of viscosity formula, and then we compare it with the dimensional analysis figures that is, M for mass, L for length, T for time.

Complete step by step answer:
Surface tension, the characteristic of a liquid surface, shown as being an elastic membrane stretched out. The almost spherical form of small drops of liquids and of soap bubbles shows this phenomenon. Some insects that stay on the surface of the water are there because of this property. Surface tension depends primarily on attractive forces between particles in the given liquid and also on the interaction between the gas, the solid or the liquid.
We know that the dimensional formula of Force F is $\left[ {ML{T^{ - 2}}} \right]$.
The dimensional formulas of length L are $\left[ {{M^0}L{T^0}} \right]$.
The dimensional formula for surface tension is:
$\begin{array}{c} \left[ T \right] = \left[ {\dfrac{{ML{T^{ - 2}}}}{{{M^0}L{T^0}}}} \right]\\\ = \left[ {M{L^0}T{}^{ - 2}} \right] \end{array}$

Therefore, the correct option is B.

Additional Information: Surface energy can be defined as excess energy on a material's surface in relation to bulk or as work required for constructing an area of a given surface. Another method of looking at the surface energy is to compare it to the work needed to cut a large sample, which produces two surfaces.

Note: During conversion it is required to be precise in basic knowledge of the formulas, it is good to break one formula into as many parts as possible. It will help to get to the result more precisely without any silly mistake.