A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$
$ML{T^{ - 3}}$ and $M{L^2}{T^{ - 4}}$
$ML{T^{ - 3}}$ and $ML{T^{ - 4}}$
$ML{T^{ - 1}}$ and $ML{T^0}$
$ML{T^{ - 4}}$ and $ML{T^1}$
If speed $V,$ area $A$ and force $F$ are chosen as fundamental units, then the dimension of Young's modulus will be :
The dimension of $\frac{\mathrm{B}^{2}}{2 \mu_{0}}$, where $\mathrm{B}$ is magnetic field and $\mu_{0}$ is the magnetic permeability of vacuum, is
If momentum $(P)$, area $(A)$ and time $(T)$ are taken to be fundamental quantities then energy has dimensional formula