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 $
$\quad 3 \quad 1 \quad 2 \quad 4 $
$\quad 3 \quad 2 \quad 1 \quad 4 $
$\quad 4 \quad 2 \quad 1 \quad 3 $
$\quad 4 \quad 1 \quad 2 \quad 3 $
Dimensional formula $M{L^{ - 1}}{T^{ - 2}}$ does not represent the physical quantity
Identify the pair whose dimensions are equal
Match List $-I$ with List $-II$
List $-I$ | List $-II$ | ||
$A$. | Coefficient of Viscosity | $I$. | $[M L^2T^{–2}]$ |
$B$. | Surface Tension | $II$. | $[M L^2T^{–1}]$ |
$C$. | Angular momentum | $III$. | $[M L^{-1}T^{–1}]$ |
$D$. | Rotational Kimeatic energy | $IV$. | $[M L^0T^{–2}]$ |
Dimension of electric current is
The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right)\,(V - b) = RT$. Here $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,\,b,\,R$ are constants. The dimensions of $'a'$ are