Question

to find the conversion factor of physical quantity in two different system of unit​

Answer 1

Answer:

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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∴1 newton=105dyne

Explanation:

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