Applying the principle of homogeneity of dimensions, determine which one is correct. where $\mathrm{T}$ is time period, $\mathrm{G}$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.
$\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}}{\mathrm{GM}^2}$
$\mathrm{T}^2=4 \pi^2 \mathrm{r}^3$
$\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^3}{G M}$
$\mathrm{T}^2=\frac{4 \pi^2 \mathrm{r}^2}{G M}$
The quantum hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge, then the dimension of $R_H$ is the same as
$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C\, ln\, (BD)$ holds true. Then which of the combination is not a meaningful quantity ?
Time period $T\,\propto \,{P^a}\,{d^b}\,{E^c}$ then value of $c$ is given $p$ is pressure, $d$ is density and $E$ is energy
Write the dimensions of $a/b$ in the relation $P = \frac{{a - {t^2}}}{{bx}}$ , where $P$ is pressure, $x$ is the distance and $t$ is the time