Question
Match the LIST-I with LIST-II
| List-I | List-II | ||
|---|---|---|---|
| A. | Spring constant | I. | $${ML}^{2}{\text{ }T}^{- 2}{\text{ }K}^{- 1}$$ |
| B. | Thermal conductivity |
II. | $${ML}^{0}{\text{ }T}^{- 2}$$ |
| C. | Boltzmann constant | III. | $${ML}^{2}{\text{ }T}^{- 3}{\text{ }A}^{- 2}$$ |
| D. | Inductive reactance | IV. | $${MLT}^{- 3}{\text{ }K}^{- 1}$$ |
Thermal
conductivity
Choose the correct answer from the options given below:
(1) A-II, B-I, C-IV, D-III
(2) A-I, B-IV, C-II, D-III
(3) A-III, B-II, C-IV, D-I
(4) A-II, B-IV, C-I, D-III
Solution
(A) $F = Kx$
$${\left\lbrack {MLT}^{- 2} \right\rbrack = \lbrack K\rbrack\lbrack L\rbrack }{\lbrack K\rbrack = {ML}^{0}{\text{ }T}^{- 2} }$$(B) Thermal conductivity
$${\frac{dQ}{dt} = \frac{kA}{\mathcal{l}}\Delta T }{{ML}^{2}{\text{ }T}^{- 3} = \frac{\lbrack k\rbrack L^{2}\text{ }K}{\text{ }L} }{\left\lbrack K^{1} \right\rbrack = {MLT}^{- 3}{\text{ }K}^{- 1} }$$(C) Boltzman constant
$$\lbrack K\rbrack = {ML}^{2}{\text{ }T}^{- 2}{\text{ }K}^{- 1} $$(D) Inductive reactance
$${\frac{\lbrack V\rbrack}{\lbrack I\rbrack} = \frac{{ML}^{2}{\text{ }T}^{- 3}{\text{ }A}^{- 1}}{\text{ }A} }{= {ML}^{2}{\text{ }T}^{- 3}{\text{ }A}^{- 2}}$$
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