Match List $I$ with List $II$ and select the correct answer using the codes given below the lists:…

Match List $I$ with List $II$ and select the correct answer using the codes given below the lists: $\begin{aligned} &\begin{array}{clcl} \text{a.} & \text{Boltzmann constant} & \text{p.} & [ML^{2}T^{-1}] \\ \text{b.} & \text{Coefficient of viscosity} & \text{q.} & [ML^{-1}T^{-1}] \\ \text{c.} & \text{Planck constant} & \text{r.} & [MLT^{-3}K^{-1}] \\ \text{d.} & \text{Thermal conductivity} & \text{s.} & [ML^{2}T^{-2}K^{-1}] \end{array} \end{aligned}$
  1. a-s;b-r;c-p;d-q;
  2. a-s;b-r;c-p;d-q;
  3. a-r;b-s;c-q;d-p;
  4. a-s;b-q;c-p;d-r;

Solution

(a) $U = \frac{1}{2} kT \Rightarrow ML^{2}T^{-2} = kK \Rightarrow K = ML^{2}T^{-2}K^{-1}$ (b) $F = \eta A \frac{dv}{dx} \Rightarrow \eta = \frac {MLT^{-2}} {L^{2} LT^{-1} L^{-1}} = ML^{-1}T^{-1}$ (c) $E = h\nu \Rightarrow ML^{2}T^{-2} = hT^{-1} \Rightarrow h = ML^{2}T^{-1}$ (d) $\frac{dQ}{dt} = \frac{kA\Delta\theta}{\ell} \Rightarrow k = \frac{ML^{2}T^{-3}L} {L^{2}K} = MLT^{-3}K^{-1}$

Asked in: JEE Advanced 2013 (Paper 2)

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