Match the physical quantities in List-I with | vedclass

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(A) $1$. Torque $(	au) = 	ext{Force} 	imes 	ext{distance} = [MLT^{-2}] 	imes [L] = [ML^2T^{-2}]$. Matches $(iv)$.$2$. Gravitational constant $(G)

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$a-iv, b-iii, c-i, d-ii$

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(A) $1$. Torque $(	au) = 	ext{Force} 	imes 	ext{distance} = [MLT^{-2}] 	imes [L] = [ML^2T^{-2}]$. Matches $(iv)$.$2$. Gravitational constant $(G)$: From $F = G \frac{m_1m_2}{r^2}$, $G = \frac{Fr^2}{m^2} = \frac{[MLT^{-2}][L^2]}{[M^2]} = [M^{-1}L^3T^{-2}]$. Matches $(iii)$.$3$. Capacitance $(C)$: From $Q = CV$, $C = \frac{Q}{V} = \frac{Q}{W/Q} = \frac{Q^2}{W} = \frac{[AT]^2}{[ML^2T^{-2}]} = [M^{-1}L^{-2}T^4A^2]$. Matches $(i)$.$4$. Planck's constant $(h)$: From $E = h
u$, $h = \frac{E}{
u} = \frac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}]$. Matches $(ii)$.Therefore, the correct matching is $a-iv, b-iii, c-i, d-ii$.

List-$I$	List-$II$
$(a)$ Torque	$(i)$ $[M^{-1}L^{-2}T^4A^2]$
$(b)$ Gravitational constant	(ii) $[M^1L^2T^{-1}]$
$(c)$ Capacitance	(iii) $[M^{-1}L^3T^{-2}]$
$(d)$ Planck's constant	(iv) $[M^1L^2T^{-2}]$

$A$. $Pa \cdot s$	$(i)$. $[L^2 T^{-2} K^{-1}]$
$B$. $N \cdot m \cdot K^{-1}$	$(ii)$. $[MLT^{-3} K^{-1}]$
$C$. $J \cdot kg^{-1} \cdot K^{-1}$	$(iii)$. $[ML^{-1} T^{-1}]$
$D$. $W \cdot m^{-1} \cdot K^{-1}$	$(iv)$. $[ML^2 T^{-2} K^{-1}]$

Column-$I$	Column-$II$
$(a)$ Wien's constant	$(i)$ $W m^{-2} K^{-4}$
$(b)$ Stefan-Boltzmann's constant	$(ii)$ $W m^{-1} K^{4}$
	$(iii)$ $m K$

$LIST$-$I$	$LIST$-$II$
$A$. Planck's constant	$I$. $ML^2T^{-2}$
$B$. Stopping potential	$II$. $T^{-1}$
$C$. Work function	$III$. $ML^2T^{-1}$
$D$. Threshold frequency	$IV$. $ML^2T^{-3}A^{-1}$

Similar Questions

The dimensions of angular momentum,latent heat,and capacitance are,respectively:

Units for constants in Column-$I$ and $SI$ unit is given in Column-$II$. Match the followings:

Column-$I$ Column-$II$

$(a)$ Wien's constant $(i)$ $W m^{-2} K^{-4}$

$(b)$ Stefan-Boltzmann's constant $(ii)$ $W m^{-1} K^{4}$

$(iii)$ $m K$

Match the following physical quantities in $LIST$-$I$ with their dimensional formulas in $LIST$-$II$:
$LIST$-$I$ $LIST$-$II$
$A$. Planck's constant $I$. $ML^2T^{-2}$
$B$. Stopping potential $II$. $T^{-1}$
$C$. Work function $III$. $ML^2T^{-1}$
$D$. Threshold frequency $IV$. $ML^2T^{-3}A^{-1}$

The pair having the same dimensions is

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