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Part of JME-07 — Units, Measurements & Error Analysis

Unit Conversion Using Dimensional Analysis

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Method: n_1 * u_1 = n_2 * u_2

If the dimensional formula is [M^a L^b T^c], then: n_2 = n_1 * (M_1/M_2)^a * (L_1/L_2)^b * (T_1/T_2)^c

Example: Convert 1 Joule to CGS units (erg). 1 J = [ML^2T^{-2}] n_2 = 1 * (1 kg / 1 g)^1 * (1 m / 1 cm)^2 * (1 s / 1 s)^{-2} n_2 = 1 * 1000 * 10000 * 1 = 10^7 So 1 J = 10^7 erg

Example: Convert G = 6.67 x 10^{-11} Nm^2/kg^2 to CGS. [G] = [M^{-1}L^3T^{-2}] n_2 = 6.67 x 10^{-11} * (10^3)^{-1} * (10^2)^3 * 1 = 6.67 x 10^{-11} * 10^{-3} * 10^6 = 6.67 x 10^{-8} So G = 6.67 x 10^{-8} dynecm^2/g^2

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