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

  • [JEE MAIN 2023]
  • A

    $\left[h^{\frac{1}{2}} c^{-\frac{1}{2}} G^1\right]$

  • B

    $\left[ h ^1 c ^1 G ^{-1}\right]$

  • C

    $\left[ h ^{-\frac{1}{2}} c ^{\frac{1}{2}} G ^{\frac{1}{2}}\right]$

  • D

    $\left[h^{\frac{1}{2}} c^{\frac{1}{2}} G ^{-\frac{1}{2}}\right]$

Similar Questions

Match List$-I$ with List$-II.$
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, $E$ $(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$
Choose the correct answer from the options given below

  • [JEE MAIN 2021]

If the time period $t$ of the oscillation of a drop of liquid of density $d$, radius $r$, vibrating under surface tension $s$ is given by the formula $t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} $ . It is observed that the time period is directly proportional to $\sqrt {\frac{d}{s}} $ . The value of $b$ should therefore be

  • [JEE MAIN 2013]

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

  • [JEE MAIN 2019]