Question

Match List I with List II

LIST I		LIST II
A	Young's Modulus (Y)	1	$\left[ M L ^{-1} T ^{-1}\right]$
B	Co-efficient of Viscosity $(\eta)$	2	$\left[ M L ^2 T ^{-1}\right]$
C	Planck's Constant (h)	3	$\left[ M L ^{-1} T ^{-2}\right]$
D	Work Function $(\phi)$	4	$\left[ M L ^{-2} T ^{-2}\right]$

Choose the correct answer from the options given below:

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

Answer 1

Answer: (D)

$Y =\frac{\text { Stress }}{\text { Strain }}=\frac{ F / A }{\Delta \ell / \ell}=\frac{\left[ MLT ^{-2}\right]}{\left[ L ^2\right]}=\left[ ML ^{-1} T ^{-2}\right] $
$ F =6 \pi \eta rv \Rightarrow \eta=\frac{ F }{6 \pi rv } $
$ {[\eta]=\frac{\left[ MLT ^{-2}\right]}{[ L ]\left[ LT ^{-1}\right]}=\left[ ML ^{-1} T ^{-1}\right]} $
$ E = hv \Rightarrow h =\frac{ E }{v}=\frac{\left[ ML ^2 T ^{-2}\right]}{\left[ T ^{-1}\right]}=\left[ ML ^2 T ^{-1}\right]$
Work function has same dimension as that of energy, so $[\phi]=\left[ ML ^2 T ^{-2}\right]$