If the velocity of light $c$, universal gravitational constant $G$ and planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is
$\left[h^{\frac{1}{2}} c^{-\frac{1}{2}} G^1\right]$
$\left[ h ^1 c ^1 G ^{-1}\right]$
$\left[ h ^{-\frac{1}{2}} c ^{\frac{1}{2}} G ^{\frac{1}{2}}\right]$
$\left[h^{\frac{1}{2}} c^{\frac{1}{2}} G ^{-\frac{1}{2}}\right]$
List$-I$ | List$-II$ |
$(a)$ Capacitance, $C$ | $(i)$ ${M}^{1} {L}^{1} {T}^{-3} {A}^{-1}$ |
$(b)$ Permittivity of free space, $\varepsilon_{0}$ | $(ii)$ ${M}^{-1} {L}^{-3} {T}^{4} {A}^{2}$ |
$(c)$ Permeability of free space, $\mu_{0}$ | $(iii)$ ${M}^{-1} L^{-2} T^{4} A^{2}$ |
$(d)$ Electric field, $E$ | $(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$ |
What is Dimensional Analysis ? State uses of Dimensional Analysis.
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
The force of interaction between two atoms is given by $F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);$ where $x$ is the distance, $k$ is the Boltzmann constant and $T$ is temperature and $\alpha $ and $\beta $ are two constants. The dimension of $\beta $ is