Density of a liquid in CGS system is 0.625 g | vedclass

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(D) The conversion formula between two systems of units is given by $N_1 U_1 = N_2 U_2$,where $N$ is the numerical value and $U$ is the unit.For densi

Vedclass · Accepted Answer

$625$

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(D) The conversion formula between two systems of units is given by $N_1 U_1 = N_2 U_2$,where $N$ is the numerical value and $U$ is the unit.For density,the dimensional formula is $[M L^{-3}]$.Given: $N_1 = 0.625$,$M_1 = 1 \ g$,$L_1 = 1 \ cm$.In $SI$ system: $M_2 = 1 \ kg = 10^3 \ g$,$L_2 = 1 \ m = 10^2 \ cm$.Using the relation $N_2 = N_1 \left[ \frac{M_1}{M_2} ight] \left[ \frac{L_1}{L_2} ight]^{-3}$:$N_2 = 0.625 	imes \left[ \frac{1 \ g}{10^3 \ g} ight] 	imes \left[ \frac{1 \ cm}{10^2 \ cm} ight]^{-3}$$N_2 = 0.625 	imes 10^{-3} 	imes (10^{-2})^{-3}$$N_2 = 0.625 	imes 10^{-3} 	imes 10^6$$N_2 = 0.625 	imes 10^3 = 625 \ kg/m^3$.Thus,the magnitude in $SI$ system is $625$.

Density of a liquid in $CGS$ system is $0.625 \ g/cm^3$. What is its magnitude in $SI$ system?

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