If momentum $(P),$ area $(A)$ and time $(T)$ are taken to be the fundamental quantities then the dimensional formula for energy is :
- [JEE MAIN 2020]
- A$\left[ PA ^{-1} T ^{-2}\right]$
- B$\left[ PA ^{1 / 2} T ^{-1}\right]$
- C$\left[ P ^{2} AT ^{-2}\right]$
- D$\left[ P ^{1 / 2} AT ^{-1}\right]$
Similar Questions
What is the dimensional formula of $a b^{-1}$ in the equation $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual meaning.
- [JEE MAIN 2024]
Number of particles is given by $n = - D\frac{{{n_2} - {n_1}}}{{{x_2} - {x_1}}}$ crossing a unit area perpendicular to $X-$axis in unit time, where ${n_1}$ and ${n_2}$ are number of particles per unit volume for the value of $x$ meant to ${x_2}$ and ${x_1}$. Find dimensions of $D$ called as diffusion constant
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
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]
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. . . . .
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. . . . .
- [IIT 2022]
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
| 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, $E$ | $(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$ |
- [JEE MAIN 2021]