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 $
If pressure $P$, velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is
In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.
A force defined by $F=\alpha t^2+\beta t$ acts on a particle at a given time $t$. The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:
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