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

The dimensions of the product $\mu_{0} \varepsilon_{0}$ are related to those of velocity as

The speed of ripples $(v)$ on a water surface depends on surface tension $(\sigma)$,density $(\rho)$,and wavelength $(\lambda)$. Then the square of speed $(v^2)$ is proportional to

If $\varepsilon_0$ is the permittivity of free space,$e$ is the charge of a proton,$G$ is the universal gravitational constant,and $m_p$ is the mass of a proton,then the dimensional formula for $\frac{e^2}{4 \pi \varepsilon_0 G m_p^2}$ is:

The electric field in a certain region is given by the formula $\vec{E} = (\frac{K}{x^3}) \hat{i}$. What is the dimensional formula of $K$?

$A$ 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: