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# Convert 5 joule into erg using dimensional analysis

Vikas TU
14149 Points
4 years ago
U must know the dimension of Joule then,
it is:
[M] [L]^2 [T]^-2
then,
1 J  = 1000 * 10000 * 1 gmcm^2/s^2 = 10^7 ergs
as for erg the unit is: gcm^2/s^2.
for 5 J  => 6*10^7 ergs.
Taani
11 Points
4 years ago
J= ML^2T^-2Using powers,a=1,b=2,c=-2We known1u1=n2u2n2=n1 [M1/M2]^a [L1/L2]^b [T1/T2]^cn2=5 [1kg/g]^1 [1m/1cm]^2 [1s/1s]^-2n2=5[1000g/1g]^1 [100cm/1cm]^2n2=5(1000) (10000)n2=5×10^7gcms^-2
Mirosh
11 Points
3 years ago
SolutionHere joule and erg are the SI unit and CGS unit of workDimension of work = [ML^2T^-2]Comipairing dimension of joule with[M^aL^bT^c] we geta=1 , b=2,c=-2Given System(SI) New system(CGS)n1=5J n2 =?M1=1kg M2=1gmL1 =1m L2=1cmT1 = 1sec T2=1 secWe known2=n1[M1/M2]^a ×[L1/L2]^b *[T1/T2]^c = 5[1kg/1g]^1×[1m/1cm]^2[1sec/1sec]^-2=5×[1000g/1g][100cm/1cm]^2×[1]^-2 = 5×1000×10000×1=5×10^7 ergTherefore 5J = 5×10^7 erg