Question

1)using dimensional analysis,show that 1 N/m square=10dynes/cm square.
2)using dimensional analysis,show that 1 joule=10 raise to 7 ergs.(numerical prblms of measurement)

Answer 1

Derivation :
1 N=10^5 dynes
1 m=100 cm
1 N/m^2=10 dynes/cm^2
1 kg*meter/sec*sec*meter^2=10 * 1000grams*100cm/sec*sec*cm^2
1 kg /sec^2 m=1 kg/sec^2 m
MLT^-2=MLT^-2                                                Hence proved..
Derivation :
1 joule=1 N m
10^7 erg=10^5dyne *10^2 cm
1 J=10^7 erg
1 kg*m^2/sec^2= 10* 1000grams*10^4cm^2/sec^2
ML^2T^-2=ML^T^-2                                           Hence proved.