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(B) The dimensional formulas are calculated as follows:$(A)$ Planck's constant $(h)$: From $E = h
u$,we have $h = E / 
u$. The dimensions of energy

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The dimensional formulas are calculated as follows:$(A)$ Planck's constant $(h)$: From $E = h
u$,we have $h = E / 
u$. The dimensions of energy $E$ are $[M^1 L^2 T^{-2}]$ and frequency $
u$ are $[T^{-1}]$. Thus,$[h] = [M^1 L^2 T^{-2}] / [T^{-1}] = [M^1 L^2 T^{-1}]$. This matches $III$.$(B)$ Stopping potential $(V_s)$: From $E = qV$,we have $V = E / q$. The dimensions of energy $E$ are $[M^1 L^2 T^{-2}]$ and charge $q$ are $[A^1 T^1]$. Thus,$[V_s] = [M^1 L^2 T^{-2}] / [A^1 T^1] = [M^1 L^2 T^{-3} A^{-1}]$. This matches $IV$.$(C)$ Work function $(\phi)$: Work function is a form of energy. Thus,$[\phi] = [M^1 L^2 T^{-2}]$. This matches $I$.$(D)$ Momentum $(p)$: Momentum $p = mv$. The dimensions are $[M^1] 	imes [L^1 T^{-1}] = [M^1 L^1 T^{-1}]$. This matches $II$.Therefore,the correct matching is $A-III, B-IV, C-I, D-II$.

List $I$	List $II$
$A$. Planck's constant $(h)$	$I$. $[M^1 L^2 T^{-2}]$
$B$. Stopping potential $(V_s)$	$II$. $[M^1 L^1 T^{-1}]$
$C$. Work function $(\phi)$	$III$. $[M^1 L^2 T^{-1}]$
$D$. Momentum $(p)$	$IV$. $[M^1 L^2 T^{-3} A^{-1}]$

Match List $I$ with List $II$:

List $I$ List $II$

$A$. Planck's constant $(h)$ $I$. $[M^1 L^2 T^{-2}]$

$B$. Stopping potential $(V_s)$ $II$. $[M^1 L^1 T^{-1}]$

$C$. Work function $(\phi)$ $III$. $[M^1 L^2 T^{-1}]$

$D$. Momentum $(p)$ $IV$. $[M^1 L^2 T^{-3} A^{-1}]$

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Match List $I$ with List $II$: List $I$ List $II$ $A$. Planck's constant $(h)$ $I$. $[M^1 L^2 T^{-2}]$ $B$. Stopping potential $(V_s)$ $II$. $[M^1 L^1 T^{-1}]$ $C$. Work function $(\phi)$ $III$. $[M^1 L^2 T^{-1}]$ $D$. Momentum $(p)$ $IV$. $[M^1 L^2 T^{-3} A^{-1}]$