(A) Surface tension is defined as force per unit length: $S = \frac{F}{\ell}$.We know that energy $K = F \cdot \ell$,so $F = \frac{K}{\ell}$.Substitut

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(A) Surface tension is defined as force per unit length: $S = \frac{F}{\ell}$.We know that energy $K = F \cdot \ell$,so $F = \frac{K}{\ell}$.Substituting this into the surface tension formula: $S = \frac{K}{\ell^2}$.Since velocity $V = \frac{\ell}{T}$,we have $\ell = V \cdot T$.Substituting $\ell$ in the expression for $S$: $S = \frac{K}{(V \cdot T)^2} = \frac{K}{V^2 T^2}$.Therefore,the dimensional formula for surface tension in terms of $K, V, T$ is $[K V^{-2} T^{-2}]$.

Class 11 Physics Units and Measurements Dimensional Analysis, Uses and Limitations

Medium

Given that $K =$ energy,$V =$ velocity,$T =$ time. If they are chosen as the fundamental units,then what is the dimensional formula for surface tension?

A
$[K V^{-2} T^{-2}]$
B
$[K^2 V^2 T^{-2}]$
C
$[K^2 V^{-2} T^{-2}]$
D
$[K V^2 T^2]$

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Dimensional Analysis, Uses and Limitations

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Given that $K =$ energy,$V =$ velocity,$T =$ time. If they are chosen as the fundamental units,then what is the dimensional formula for surface tension?

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$A$ quantity $x$ is given by $(IF v^{2} / WL^{4})$ in terms of moment of inertia $I$,force $F$,velocity $v$,work $W$,and length $L$. The dimensional formula for $x$ is the same as that of:

If $z = xP + G$,where $P$ is pressure and $G$ is the universal gravitational constant; then the dimensional formulas for $x$ and $z$ respectively are (here,$G = \frac{Fr^2}{m_1 m_2}$,$P = \frac{\text{Thrust}}{\text{Area}}$).

What could be a correct expression for the speed of ocean waves in terms of its wavelength $\lambda$,the depth $h$ of the ocean,the density $\rho$ of sea water,and the acceleration of free fall $g$?

If the acceleration due to gravity is $10\,m/s^2$ and the units of length and time are changed to kilometer and hour respectively,the numerical value of the acceleration is

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