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
$M L^{-1} T^{-2}$
$\mathrm{ML}^{2} \mathrm{T}^{-1}$
$\mathrm{ML} \mathrm{T}^{-2}$
$\mathrm{ML}^{2} \mathrm{T}^{-2}$
Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of $L$, which of the following statement ($s$) is/are correct ?
$(1)$ The dimension of force is $L ^{-3}$
$(2)$ The dimension of energy is $L ^{-2}$
$(3)$ The dimension of power is $L ^{-5}$
$(4)$ The dimension of linear momentum is $L ^{-1}$
In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is
A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ' $\eta$ ' flowing per second, through a tube of radius $r$ and length / and having a pressure difference $P$ across its ends, is
List$-I$ | List$-II$ |
$(a)$ Magnetic Induction | $(i)$ ${ML}^{2} {T}^{-2} {A}^{-1}$ |
$(b)$ Magnetic Flux | $(ii)$ ${M}^{0} {L}^{-1} {A}$ |
$(c)$ Magnetic Permeability | $(iii)$ ${MT}^{-2} {A}^{-1}$ |
$(d)$ Magnetization | $(iv)$ ${MLT}^{-2} {A}^{-2}$ |
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