Let $[{\varepsilon _0}]$ denotes the dimensional formula of the permittivity of the vacuum and $[{\mu _0}]$ that of the permeability of the vacuum. If $M = {\rm{mass}}$, $L = {\rm{length}}$, $T = {\rm{Time}}$ and $I = {\rm{electric current}}$, then
Let $[{\varepsilon _0}]$ denotes the dimensional formula of the permittivity of the vacuum and $[{\mu _0}]$ that of the permeability of the vacuum. If $M = {\rm{mass}}$, $L = {\rm{length}}$, $T = {\rm{Time}}$ and $I = {\rm{electric current}}$, then
- [IIT 1998]
- A
$[{\varepsilon _0}] = {M^{ - 1}}{L^{ - 3}}{T^2}I$
- B
$[{\varepsilon _0}] = {M^{ - 1}}{L^{ - 3}}{T^4}{I^2}$
- C
$[{\mu _0}] = M{L^2}{T^{ - 1}}I$
- D
None of these
Similar Questions
In equation $y=x^2 \cos ^2 2 \pi \frac{\beta \gamma}{\alpha}$, the units of $x, \alpha, \beta$ are $m , s ^{-1}$ and $\left( ms ^{-1}\right)^{-1}$ respectively. The units of $y$ and $\gamma$ are
In the relation $y = a\cos (\omega t - kx)$, the dimensional formula for $k$ is
In the relation $y = a\cos (\omega t - kx)$, the dimensional formula for $k$ is
Young-Laplace law states that the excess pressure inside a soap bubble of radius $R$ is given by $\Delta P=4 \sigma / R$, where $\sigma$ is the coefficient of surface tension of the soap. The EOTVOS number $E_0$ is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of $g$, the acceleration due to gravity $\rho$ the density of the surrounding fluid $\sigma$ and a characteristic length scale $L$ which could be the radius of the bubble. A possible expression for $E_0$ is
Young-Laplace law states that the excess pressure inside a soap bubble of radius $R$ is given by $\Delta P=4 \sigma / R$, where $\sigma$ is the coefficient of surface tension of the soap. The EOTVOS number $E_0$ is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of $g$, the acceleration due to gravity $\rho$ the density of the surrounding fluid $\sigma$ and a characteristic length scale $L$ which could be the radius of the bubble. A possible expression for $E_0$ is
- [KVPY 2013]
Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :
List $I$
List $II$
$P.$ Boltzmann constant
$1.$ $\left[ ML ^2 T ^{-1}\right]$
$Q.$ Coefficient of viscosity
$2.$ $\left[ ML ^{-1} T ^{-1}\right]$
$R.$ Planck constant
$3.$ $\left[ MLT ^{-3} K ^{-1}\right]$
$S.$ Thermal conductivity
$4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$
Codes: $ \quad \quad P \quad Q \quad R \quad S $
Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :
| List $I$ | List $II$ |
| $P.$ Boltzmann constant | $1.$ $\left[ ML ^2 T ^{-1}\right]$ |
| $Q.$ Coefficient of viscosity | $2.$ $\left[ ML ^{-1} T ^{-1}\right]$ |
| $R.$ Planck constant | $3.$ $\left[ MLT ^{-3} K ^{-1}\right]$ |
| $S.$ Thermal conductivity | $4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$ |
Codes: $ \quad \quad P \quad Q \quad R \quad S $
- [IIT 2013]
The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C\,{m^x}{K^y}$; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are
The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C\,{m^x}{K^y}$; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are
- [AIPMT 1990]