The dimensions of $K$ in the equation $W = \frac{1}{2}\,\,K{x^2}$ is
${M^1}{L^0}{T^{ - 2}}$
${M^0}{L^1}{T^{ - 1}}$
${M^1}{L^1}{T^{ - 2}}$
${M^1}{L^0}{T^{ - 1}}$
In the relation : $\frac{d y}{d x}=2 \omega \sin \left(\omega t+\phi_0\right)$ the dimensional formula for $\left(\omega t+\phi_0\right)$ is :
A system has basic dimensions as density $[D]$, velocity $[V]$ and area $[A]$. The dimensional representation of force in this system is
Young-Laplace law states that the excess pressure inside a soap bubble of radius $R$ is given by $\Delta P=4 \sigma / R$, where $\sigma$ is the coefficient of surface tension of the soap. The EOTVOS number $E_0$ is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of $g$, the acceleration due to gravity $\rho$ the density of the surrounding fluid $\sigma$ and a characteristic length scale $L$ which could be the radius of the bubble. A possible expression for $E_0$ is