The dimensional formula of wave number is
The dimensional formula of wave number is
- A
${M^0}{L^0}{T^{ - 1}}$
- B
${M^0}{L^{ - 1}}{T^0}$
- C
${M^{ - 1}}{L^{ - 1}}{T^0}$
- D
${M^0}{L^0}{T^0}$
Similar Questions
Match List$-I$ with List$-II$.
List$-I$
List$-II$
$(A)$ Angular momentum
$(I)$ $\left[ ML ^2 T ^{-2}\right]$
$(B)$ Torque
$(II)$ $\left[ ML ^{-2} T ^{-2}\right]$
$(C)$ Stress
$(III)$ $\left[ ML ^2 T ^{-1}\right]$
$(D)$ Pressure gradient
$(IV)$ $\left[ ML ^{-1} T ^{-2}\right]$
Choose the correct answer from the options given below:
Match List$-I$ with List$-II$.
| List$-I$ | List$-II$ |
| $(A)$ Angular momentum | $(I)$ $\left[ ML ^2 T ^{-2}\right]$ |
| $(B)$ Torque | $(II)$ $\left[ ML ^{-2} T ^{-2}\right]$ |
| $(C)$ Stress | $(III)$ $\left[ ML ^2 T ^{-1}\right]$ |
| $(D)$ Pressure gradient | $(IV)$ $\left[ ML ^{-1} T ^{-2}\right]$ |
Choose the correct answer from the options given below:
- [JEE MAIN 2023]
In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E]$ and $[B]$ stand for dimensions of electric and magnetic fields respectively, while $\left[\varepsilon_0\right]$ and $\left[\mu_0\right]$ stand for dimensions of the permittivity and permeability of free space respectively. $[L]$ and $[T]$ are dimensions of length and time respectively. All the quantities are given in $SI$ units.
($1$) The relation between $[E]$ and $[B]$ is
$(A)$ $[ E ]=[ B ][ L ][ T ]$ $(B)$ $[ E ]=[ B ][ L ]^{-1}[ T ]$ $(C)$ $[ E ]=[ B ][ L ][ T ]^{-1}$ $(D)$ $[ E ]=[ B ][ L ]^{-1}[ T ]^{-1}$
($2$) The relation between $\left[\varepsilon_0\right]$ and $\left[\mu_0\right]$ is
$(A)$ $\left[\mu_0\right]=\left[\varepsilon_0\right][ L ]^2[ T ]^{-2}$ $(B)$ $\left[\mu_0\right]=\left[\varepsilon_0\right][ L ]^{-2}[ T ]^2$ $(C)$ $\left[\mu_0\right]=\left[\varepsilon_0\right]^{-1}[ L ]^2[ T ]^{-2}$ $(D)$ $\left[\mu_0\right]=\left[\varepsilon_0\right]^{-1}[ L ]^{-2}[ T ]^2$
Give the answer or quetion ($1$) and ($2$)
In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E]$ and $[B]$ stand for dimensions of electric and magnetic fields respectively, while $\left[\varepsilon_0\right]$ and $\left[\mu_0\right]$ stand for dimensions of the permittivity and permeability of free space respectively. $[L]$ and $[T]$ are dimensions of length and time respectively. All the quantities are given in $SI$ units.
($1$) The relation between $[E]$ and $[B]$ is
$(A)$ $[ E ]=[ B ][ L ][ T ]$ $(B)$ $[ E ]=[ B ][ L ]^{-1}[ T ]$ $(C)$ $[ E ]=[ B ][ L ][ T ]^{-1}$ $(D)$ $[ E ]=[ B ][ L ]^{-1}[ T ]^{-1}$
($2$) The relation between $\left[\varepsilon_0\right]$ and $\left[\mu_0\right]$ is
$(A)$ $\left[\mu_0\right]=\left[\varepsilon_0\right][ L ]^2[ T ]^{-2}$ $(B)$ $\left[\mu_0\right]=\left[\varepsilon_0\right][ L ]^{-2}[ T ]^2$ $(C)$ $\left[\mu_0\right]=\left[\varepsilon_0\right]^{-1}[ L ]^2[ T ]^{-2}$ $(D)$ $\left[\mu_0\right]=\left[\varepsilon_0\right]^{-1}[ L ]^{-2}[ T ]^2$
Give the answer or quetion ($1$) and ($2$)
- [IIT 2018]
The dimension of magnetic field in $M, L, T$ and $C$ (coulomb) is given as
The dimension of magnetic field in $M, L, T$ and $C$ (coulomb) is given as
- [AIEEE 2008]
A system has basic dimensions as density $[D]$, velocity $[V]$ and area $[A]$. The dimensional representation of force in this system is
A system has basic dimensions as density $[D]$, velocity $[V]$ and area $[A]$. The dimensional representation of force in this system is
If momentum $[ P ]$, area $[ A ]$ and time $[ T ]$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :
If momentum $[ P ]$, area $[ A ]$ and time $[ T ]$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :
- [JEE MAIN 2022]