The density of a material in CGS system of un | vedclass

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Question

(C) The principle of dimensional consistency states that the magnitude of a physical quantity remains constant regardless of the system of units used,

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(C) The principle of dimensional consistency states that the magnitude of a physical quantity remains constant regardless of the system of units used,expressed as $n_1 u_1 = n_2 u_2$.Here,the density $ho = 4 \, g \, cm^{-3}$.In the new system,the unit of mass $M_2 = 100 \, g$ and the unit of length $L_2 = 10 \, cm$.The density in the new system is given by $ho = n_2 \frac{M_2}{L_2^3}$.Substituting the values: $4 \, g \, cm^{-3} = n_2 \frac{100 \, g}{(10 \, cm)^3}$.$4 = n_2 \frac{100}{1000}$.$4 = n_2 	imes 0.1$.$n_2 = \frac{4}{0.1} = 40$.

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

The density of a material in $CGS$ system of units is $4 \, g \, cm^{-3}$. In a system of units in which the unit of length is $10 \, cm$ and the unit of mass is $100 \, g$,the value of the density of the material will be:

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