Force $F$ is given in terms of time $t$ and distance $x$ by $F = a\, sin\, ct + b\, cos\, dx$, then the dimension of $a/b$ is
$[M^0L^0T^0]$
$[M^0L^1T^{-1}]$
$[M^0L^1T^0]$
$[M^1L^1T^{-2}]$
The dimension of $P = \frac{{{B^2}{l^2}}}{m}$ is
where $B=$ magnetic field, $l=$ length, $m =$ mass
Planck's constant $(h),$ speed of light in vacuum $(c)$ and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length $?$
The dimensional formula of permeability of free space $\mu_0$ is
If ${E}, {L}, {m}$ and ${G}$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of ${P}$ in the formula ${P}={EL}^{2} {m}^{-5} {G}^{-2}$ are
The dimensions of ${\left( {{\mu _0}{\varepsilon _0}} \right)^{ - \frac{1}{2}}}$ are