Question

Names of units of some physical quantities are given in List-I and their dimensions formulae are given in List-Il. Match the correct pairs in the lists

List-I		List-II
A	$Pa-s$	(i)	$\left[ L ^{2} T ^{-2} K ^{-1}\right]$
B	$NmK^{− 1}$	(ii)	$\left[ MLT ^{-3} K ^{-1}\right]$
C	$J \,kg ^{-1} K ^{-1}$	(iii)	$\left[ ML ^{-1} T ^{-1}\right]$
D	$Wm ^{-1} K ^{-1}$	(iv)	$\left[ ML ^{2} T ^{-2} K ^{-1}\right]$

• A. A - (iv), B - (iii),C - (i),D - (ii)
• B. A - (iii),B - (ii), C - (iv), D - (i)
• C. A - (iii),B - (i), C - (iv), D - (ii)
• D. A - (iii), B - (iv), C - (i),D - (ii)

Answer 1

Answer: (D)

Dimensions of $Pa-s$ is
$=\left[ ML ^{-1} T ^{-2}\right] \cdot[ T ] $
$=\left[ ML ^{-1} T ^{-1}\right]$
Dimensions of $NmK ^{-1}$ is
$=\left[ MLT ^{-2}\right][ L ][ K ]^{-1}$
$=\left[ ML ^{2} T ^{-2} K ^{-1}\right]$
Dimensions of $Jkg ^{-1} K ^{-1}$
$=\left[ ML ^{2} T ^{-2}\right][ M ]^{-1}[ K ]^{-1} $
$=\left[ L ^{2} T ^{-2} K ^{-1}\right]$
Dimensions of $Wm ^{-1} K ^{-1}$
$=\left[ ML ^{2} T ^{-3}\right][ L ]^{-1}[ K ]^{-1}$
$=\left[ MLT ^{-3} K ^{-1}\right]$
So, the correct matching is (iii), (iv), (i), (ii),