The dimensions of physical quantity $X$ in the equation Force $ = \frac{X}{{{\rm{Density}}}}$ is given by
${M^1}{L^4}{T^{ - 2}}$
${M^2}{L^{ - 2}}{T^{ - 1}}$
${M^2}{L^{ - 2}}{T^{ - 2}}$
${M^1}{L^{ - 2}}{T^{ - 1}}$
In a particular system of units, a physical quantity can be expressed in terms of the electric charge $c$, electron mass $m_c$, Planck's constant $h$, and Coulomb's constant $k=\frac{1}{4 \pi \epsilon_0}$, where $\epsilon_0$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is $[B]=[c]^\alpha\left[m_c\right]^\beta[h]^\gamma[k]^\delta$. The value of $\alpha+\beta+\gamma+\delta$ is. . . . .
Using dimensional analysis, the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as
If speed $(V)$, acceleration $(A)$ and force $(F)$ are considered as fundamental units, the dimension of Young’s modulus will be
Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ are
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 $L ^{-1}$