Basic Maths and Units and DimensionsMedium

Question

Match List-I with List-II.

List-I List-II
A. Boltzmann constant I. $$\left\lbrack M^{- 1}{\text{ }L}^{3}{\text{ }T}^{- 2} \right\rbrack$$
B. Stefan's constant II. $$\left\lbrack ML^{2}{\text{ }T}^{- 1} \right\rbrack$$
C. Planck's constant III. $$\left\lbrack {ML}^{2}{\text{ }T}^{- 2}{\text{ }K}^{- 1} \right\rbrack$$
D.

Gravitational

constant

 IV. $$\left\lbrack {ML}^{0}{\text{ }T}^{- 3}{\text{ }K}^{- 4} \right\rbrack$$

Gravitational

constant

Options

A.A-I, B-II,C-III, D-IV
B.A-IV, B-III,C-II, D-I
C.A-III, B-IV,C-II, D-I
D.A-II, B-I,C-IV, D-III

Solution

Sol. [Key Concept: Match by dimensions: Boltzmann $\lbrack{ML}^{2}T^{- 2}K^{- 1}\rbrack$, Stefan $\lbrack{MT}^{- 3}K^{- 4}\rbrack$, Planck $\lbrack{ML}^{2}T^{- 1}\rbrack$, gravitational $\lbrack M^{- 1}L^{3}T^{- 2}\rbrack$.]

(A) $\rightarrow {ML}^{2}{\text{ }T}^{- 2}{\text{ }K}^{- 1}$

(B) $\rightarrow {MT}^{- 3}{\text{ }K}^{- 4}$

(C) $\rightarrow {ML}^{2}{\text{ }T}^{- 1}$

(D) $\rightarrow M^{- 1}{\text{ }L}^{3}{\text{ }T}^{- 2}$

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