Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be
$\left[ M \right] = \left[ {{T^{ - 1}}\,{C^{ - 2}}\,h} \right]$
$\left[ M \right] = \left[ {{T^{ - 1}}\,{C^2}\,h} \right]$
$\left[ M \right] = \left[ {{T^{ - 1}}\,{C^{ - 2}}\,{h^{ - 1}}} \right]$
$\left[ M \right] = \left[ {T\,{C^{ - 2}}\,h} \right]$
If $G$ is universal gravitation constant and $g$ is acceleration due to gravity, then dimensions of $\frac{G}{g}$ will be ...................
Identify the pair of physical quantities which have different dimensions
Dimensions of the following three quantities are the same
The displacement of a progressive wave is represented by $y = A\,sin \,(\omega t - kx)$ where $x$ is distance and t is time. Write the dimensional formula of $(i)$ $\omega $ and $(ii)$ $k$.
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants $G, h$ and $c$ . Which of the following correctly gives the Planck length?