Question

using Dimensions Show that 1 Joule =10^7 erg ? Ans

Answer 1

1 joule = kgm^2s^-2 Ergs follows =gcm^2s^-2(cgs unit) n1u1=n2u2( where n is numerical value and u is unit) N1U1=N2U2 1*kgm^2s^-2=n2*gcm^2s^-2 N2=1*kgm^2cm^-2/gcm^2s^-2 Convert SI units to cgs units 1 kg=1000g,1m =100cm,1s=1s only So ,  N2=1*1000g*(100)^2cm^2*s^-2/gcm^2*s^-2  Cancel the units finally  N2 = 1*1000*10000=10^7  10^7 is numerical value  Hence proved!!