Question 54: Units , Dimensions and Error Analysis

Question

Match List I with List II.

List - I

List - II

(A)
Coefficient of viscosity
(I)
$\left[\mathrm{ML}^0 \mathrm{~T}^{-3}\right]$

(B)
Intensity of wave
(II)
$\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right]$

(C)
Pressure gradient
(III)
$\left[\mathrm{M}^{-1} \mathrm{LT}^2\right]$

(D)
Compressibility
(IV)
$\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$

Choose the correct answer from the options given below:

Accepted Answer

Here are the dimensional formulas:
Coefficient of viscosity, ÃÂ¼
$$[\mu]=\frac{	ext{pressure}	imes	ext{time}}{}     =\frac{[M\,L^{-1}T^{-2}]\,[T]}{}     =[M\,L^{-1}T^{-1}]\quad\longrightarrow	ext{(IV)}$$
Intensity of a wave, I
$$[I]=\frac{	ext{power}}{	ext{area}}     =\frac{[M\,L^2T^{-3}]}{[L^2]}     =[M\,L^0T^{-3}]\quad\longrightarrow	ext{(I)}$$
Pressure gradient, dP/dx
$$\left[\frac{dP}{dx}ight]    =\frac{[M\,L^{-1}T^{-2}]}{[L]}    =[M\,L^{-2}T^{-2}]\quad\longrightarrow	ext{(II)}$$
Compressibility, ÃÂº
$$[\kappa]=\frac1{[	ext{pressure}]}    =[M^{-1}L\,T^2]\quad\longrightarrow	ext{(III)}$$
Matching gives
(A)Ã¢ÂÂ(IV), (B)Ã¢ÂÂ(I), (C)Ã¢ÂÂ(II), (D)Ã¢ÂÂ(III), i.e.
Option C
.

Answer

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

Answer

(A)-(IV), (B)-(II), (C)-(I), (D)-(III)

Answer

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

Answer

(A)-(I), (B)-(IV), (C)-(III), (D)-(II)

Units , Dimensions and Error Analysis

Choose the correct answer: