Match List I with List II and select the correct answer using the codes given below the lists: cases & -I & & & -II a. & Boltzmann constant & & p. & [ ML^ 2 T^ -1 ] b. & Coefficient of viscosity & & q. & [ ML^ -1 T^ -1

Correct answer: D. a-s;b-q;c-p;d-r; (a) U = (1)/(2)kT ⇒ ML ^ 2 T ^ - 2 = [k]K ⇒ [K] = ML ^ 2 T ^ - 2 K ^ -1 (b) F = ηA(dv)/(dx) ⇒ [η] = MLT ^ - 2 L ^ 2 LT ^ -1 L ^ -1 = ML ^ -1 T ^ -1 (c) E = hν ⇒ ML ^ 2 T ^ - 2 = [h] T ^ -1 ⇒ [h] = ML ^ 2 T ^ -1 (d) (dQ)/(dt) = (kA Δ θ)/(ℓ) ⇒ [k] = ML ^ 2 T ^ - 3 L L ^ 2 K = MLT ^ - 3 K ^ -1

NEET

Exam: NEET
Subject: Physics
Chapter: Units and Dimensions

NEET · Physics · Units and Dimensions

Match List I with List II and select the correct answer using the...

Match List

I

with List

II

and select the correct answer using the codes given below the lists:

\begin{cases} & \textList-I & & & \textList-II \\ \text{a.} & \text{Boltzmann constant} & & \text{p.} & \left[{\text{ML}^{2}{\text{T}^{-1}\right] \\ \text{b.} & \text{Coefficient of viscosity} & & \text{q.} & \left[{\text{ML}^{-1}{\text{T}^{-1}\right] \\ \text{c.} & \text{Planck constant} & & \text{r.} & \left[{\text{MLT}^{- 3}{\text{K}^{-1}\right] \\ \text{d.} & \text{Thermal conductivity} & & \text{s.} & \left[{\text{ML}^{2}{\text{T}^{- 2}{\text{K}^{-1}\right]\end{cases}

Options

Aa-s;b-r;c-p;d-q;
Ba-s;b-r;c-p;d-q;
Ca-r;b-s;c-q;d-p;
Da-s;b-q;c-p;d-r;

Correct answer

D. a-s;b-q;c-p;d-r;

Step-by-step solution

(a)

U = \dfrac{1}{2}kT ⇒ {\text{ML}}^{2}{\text{T}}^{- 2} = \left[\text{k}\right]\text{K} ⇒ \left[\text{K}\right] = {\text{ML}}^{2}{\text{T}}^{- 2}{\text{K}}^{-1}

(b)

F = ηA\dfrac{dv}{dx} ⇒ \left[η\right] = \dfrac{{\text{MLT}}^{- 2}}{{\text{L}}^{2}{\text{LT}}^{-1}{\text{L}}^{-1}} = {\text{ML}}^{-1}{\text{T}}^{-1}

(c)

E = hν ⇒ {\text{ML}}^{2}{\text{T}}^{- 2} = \left[\text{h}\right]{\text{T}}^{-1} ⇒ \left[\text{h}\right] = {\text{ML}}^{2}{\text{T}}^{-1}

(d)

\dfrac{dQ}{dt} = \dfrac{kA \Delta \theta}{ℓ} ⇒ \left[\text{k}\right] = \dfrac{{\text{ML}}^{2}{\text{T}}^{- 3}\text{L}}{{\text{L}}^{2}\text{K}} = {\text{MLT}}^{- 3}{\text{K}}^{-1}

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