The density of a material in SI units is 128 | vedclass

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(A) The formula for conversion between two systems of units is $n_2 = n_1 \left( \frac{M_1}{M_2} \right)^a \left( \frac{L_1}{L_2} \right)^b \left( \fr

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$40$

Vedclass · Answer

(A) The formula for conversion between two systems of units is $n_2 = n_1 \left( \frac{M_1}{M_2} ight)^a \left( \frac{L_1}{L_2} ight)^b \left( \frac{T_1}{T_2} ight)^c$.Here,the dimension of density is $[M^1 L^{-3} T^0]$,so $a=1, b=-3, c=0$.Given: $n_1 = 128$,$M_1 = 1 \ kg = 1000 \ g$,$L_1 = 1 \ m = 100 \ cm$.New units: $M_2 = 50 \ g$,$L_2 = 25 \ cm$.Substituting the values:$n_2 = 128 	imes \left( \frac{1000 \ g}{50 \ g} ight)^1 	imes \left( \frac{100 \ cm}{25 \ cm} ight)^{-3}$$n_2 = 128 	imes (20) 	imes (4)^{-3}$$n_2 = 128 	imes 20 	imes \frac{1}{64}$$n_2 = 2 	imes 20 = 40$.

The density of a material in $SI$ units is $128 \ kg \ m^{-3}$. In a system of units where the unit of length is $25 \ cm$ and the unit of mass is $50 \ g$,the numerical value of the density of the material is:

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