The dimensional formula of $\frac{1}{\mu_{0} \varepsilon_{0}}$ is . . . . . . .

The equation of a wave is given by $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,where $\omega$ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is

The energy $(E)$, angular momentum $(L)$, and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of the universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is

$A$ flywheel can rotate in order to store kinetic energy. The flywheel is a uniform disk made of a material with a density $\rho$ and tensile strength $\sigma$ (measured in Pascals),a radius $r$,and a thickness $h$. The flywheel is rotating at the maximum possible angular velocity so that it does not break. Which of the following expressions correctly gives the maximum kinetic energy per kilogram that can be stored in the flywheel? Assume that $\alpha$ is a dimensionless constant.

What is dimensional analysis? Write the limitations of dimensional analysis.

If the force is given by $F = at + bt^2$ where $t$ is time, the dimensions of $a$ and $b$ are: