$A$ system has basic dimensions as density $[D]$,velocity $[V]$,and area $[A]$. The dimensional representation of force in this system is:

$A$ 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:

Consider the equation $\frac{1}{2} m v^{2} = m g h$,where $m$ is the mass of the body,$v$ is the velocity,$g$ is the acceleration due to gravity,and $h$ is the height. Is this equation dimensionally correct?

Write and explain the principle of homogeneity. Check the dimensional consistency of the given equation: $x = x_{0} + v_{0}t + \frac{1}{2}at^{2}$.

Given that: $\lambda = a \cos \left( \frac{t}{p} - qx \right)$,where $t$ represents time in $s$ and $x$ represents distance in $m$. Which of the following statements is true?

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 $g$?