Match List I with List II and select the correct answer using the… - Vidyadip

Question

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 $

✓

Answer

$(p)$ $U =\frac{1}{2} kT \quad \Rightarrow \quad ML ^2 T ^{-2}=[ k ] K \quad \Rightarrow \quad[ K ]= ML ^2 T ^{-2} K ^{-1}$

$(q)$ $F =\eta A \frac{ dv }{ dx } \Rightarrow \quad[\eta]=\frac{ MLT ^{-2}}{ L ^2 LT ^{-1} L ^{-1}}= ML ^{-1} T ^{-1}$

$(r)$ $E = h v \quad \Rightarrow \quad ML ^2 T ^2=[ h ] T ^{-1} \Rightarrow \quad[ h ]= ML ^2 T ^{-1}$

$(s)$ $\frac{ dQ }{ dt }=\frac{ kA \Delta \theta}{\ell} \Rightarrow \quad[ k ]=\frac{ ML ^2 T ^{-3} L }{ L ^2 K }= MLT ^{-3} K ^{-1}$

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