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Convert 5 joule into erg using dimensional analysis

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4 years ago

Vikas TU
14146 Points
```							U must know the dimension of Joule then,it is:[M] [L]^2 [T]^-2then,1 J  = 1000 * 10000 * 1 gmcm^2/s^2 = 10^7 ergsas for erg the unit is: gcm^2/s^2.for 5 J  => 6*10^7 ergs.
```
4 years ago
Taani
11 Points
```							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
```
3 years ago
Mirosh
11 Points
```							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
```
3 years ago
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