If orbital velocity of planet is given by $v = {G^a}{M^b}{R^c}$, then
$a = 1/3,\,b = 1/3,\,c = - 1/3$
$a = 1/2,\,b = 1/2,\,c = - 1/2$
$a = 1/2,\,b = - 1/2,\,c = 1/2$
$a = 1/2,\,b = - 1/2,\,c = - 1/2$
If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$, radius $(r)$ of the drop and density $(\rho )$ of the liquid, then the expression of $T$ is
In terms of potential difference $V$, electric current $I$, permittivity $\varepsilon_0$, permeability $\mu_0$ and speed of light $c$, the dimensionally correct equation$(s)$ is(are)
$(A)$ $\mu_0 I ^2=\varepsilon_0 V ^2$ $(B)$ $\varepsilon_0 I =\mu_0 V$ $(C)$ $I =\varepsilon_0 cV$ $(D)$ $\mu_0 cI =\varepsilon_0 V$
The dimensions of Planck's constant and angular momentum are respectively
The dimensions of $\frac{\alpha}{\beta}$ in the equation $F=\frac{\alpha-t^2}{\beta v^2}$, where $F$ is the force, $v$ is velocity and $t$ is time, is ..........
Using dimensional analysis, the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as