Question

derive the formula conversion of physical quantity from one system of unit into another

Answer 1

To find conversion factor between the units of the same physical quantity in two different systems of units.

e.g. To find the conversion factor between the units of Force. i.e. newton in SI system to dyne in c.g.s. system

Let 1 newton = x dyne               ....(i)

The dimensions of force are [L1M1T−2]L1M1T-2

∴∴ equation (1) in dimension form can be written as

[L11M1 1T−21=x[L21M2 1T−22][L11M1 1T1-2=xL21M2 1T2-2

∴x=[L11M11T−21][L21M11T−21]∴x=L11M11T1-2L21M11T1-2

=(L1L2)1(M1M2)1(T1T2)−2=L1L21M1M21T1T2-2           ...(ii)

where suffix 1 indicates SI system and suffix 2 indicates C.G.S. system.

In S.I. system L, M and T are expressed in m, kg, s and in C.G.S. system L, M and T are expressed in cm, g and s respectively,

equation (ii) becomes

x=(mcm)1(kgg)1(ss)−2x=mcm1kgg1ss-2

=(102cmcm)1(103gg)1(1)−2=102cmcm1103gg11-2

∴x=105∴x=105

∴1 newton=105dyne


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