The units of length,velocity,and force are do | vedclass

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(C) Let the original units be $L$,$v$,and $F$. The new units are $L' = 2L$,$v' = 2v$,and $F' = 2F$.We know that velocity $v = L/T$,so the unit of time

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Unit of momentum is doubled

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(C) Let the original units be $L$,$v$,and $F$. The new units are $L' = 2L$,$v' = 2v$,and $F' = 2F$.We know that velocity $v = L/T$,so the unit of time $T = L/v$. The new unit of time $T' = L'/v' = (2L)/(2v) = L/v = T$. Thus,the unit of time remains unchanged.We know that force $F = ma = m(v/T)$,so the unit of mass $m = FT/v$. The new unit of mass $m' = F'T'/v' = (2F 	imes T)/(2v) = FT/v = m$. Thus,the unit of mass remains unchanged.We know that momentum $p = mv$. The new unit of momentum $p' = m'v' = m 	imes (2v) = 2mv = 2p$. Thus,the unit of momentum is doubled.We know that energy $E = F 	imes L$. The new unit of energy $E' = F' 	imes L' = (2F) 	imes (2L) = 4FL = 4E$. Thus,the unit of energy becomes four times the original value.Therefore,the correct statement is that the unit of momentum is doubled.

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-$II$
$(a)$ Capacitance,$C$	$(i)$ $M^{1} L^{1} T^{-3} A^{-1}$
$(b)$ Permittivity of free space,$\varepsilon_{0}$	$(ii)$ $M^{-1} L^{-3} T^{4} A^{2}$
$(c)$ Permeability of free space,$\mu_{0}$	$(iii)$ $M^{-1} L^{-2} T^{4} A^{2}$
$(d)$ Electric field,$E$	$(iv)$ $M^{1} L^{1} T^{-2} A^{-2}$

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

The units of length,velocity,and force are doubled. Which of the following is the correct change in the other units?

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

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

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