Let $[ {\varepsilon _0} ]$ denote the dimensional formula of the permittivity of vacuum. If $M =$ mass, $L=$ length, $T =$ time and $A=$ electric current, then:
- [JEE MAIN 2013]
- A$[ {\varepsilon _0} ]=[M^{-1}L^{-3}T^2A]$
- B$[ {\varepsilon _0} ]=[M^{-1}L^{-3}T^4A^2]$
- C$[ {\varepsilon _0} ]=[M^{-1}L^2T^{-1}A^{-2}]$
- D$[ {\varepsilon _0} ]=[M^{-1}L^2T^{-1}A]$
Similar Questions
The equation of state of a real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where $\mathrm{P}, \mathrm{V}$ and $\mathrm{T}$ are pressure. volume and temperature respectively and $R$ is the universal gas constant. The dimensions of $\frac{a}{b^2}$ is similar to that of :
The equation of state of a real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where $\mathrm{P}, \mathrm{V}$ and $\mathrm{T}$ are pressure. volume and temperature respectively and $R$ is the universal gas constant. The dimensions of $\frac{a}{b^2}$ is similar to that of :
- [JEE MAIN 2024]
If force $(F)$, length $(L) $ and time $(T)$ are assumed to be fundamental units, then the dimensional formula of the mass will be
If force $(F)$, length $(L) $ and time $(T)$ are assumed to be fundamental units, then the dimensional formula of the mass will be
An expression for a dimensionless quantity $P$ is given by $P=\frac{\alpha}{\beta} \log _{e}\left(\frac{ kt }{\beta x }\right)$; where $\alpha$ and $\beta$ are constants, $x$ is distance ; $k$ is Boltzmann constant and $t$ is the temperature. Then the dimensions of $\alpha$ will be
- [JEE MAIN 2022]
Consider following statements
$(A)$ Any physical quantity have more than one unit
$(B)$ Any physical quantity have only one dimensional formula
$(C)$ More than one physical quantities may have same dimension
$(D)$ We can add and subtract only those expression having same dimension
Number of correct statement is
Consider following statements
$(A)$ Any physical quantity have more than one unit
$(B)$ Any physical quantity have only one dimensional formula
$(C)$ More than one physical quantities may have same dimension
$(D)$ We can add and subtract only those expression having same dimension
Number of correct statement is
If ${E}, {L}, {m}$ and ${G}$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of ${P}$ in the formula ${P}={EL}^{2} {m}^{-5} {G}^{-2}$ are
If ${E}, {L}, {m}$ and ${G}$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of ${P}$ in the formula ${P}={EL}^{2} {m}^{-5} {G}^{-2}$ are
- [JEE MAIN 2021]