Physics

To find the convergence factor between the units of same physical quantities in two different system 


SOLUTION

To find the conversion factor b/w the units of force-

i.e newton in si system to dyne is cgs system-

in  x dyne

dimension of force are  $$\left[ {{L^1}{M^1}{T^{ - 2}}} \right]$$

$$\left[ {{L_1}^1{M_1}^1{T_1}^{ - 2}} \right] = X\left[ {{L_2}^1{M_2}^1{T_2}^{ - 2}} \right]$$

$$X = {\left( {{{{L_1}} \over {{L_2}}}} \right)^{ + 1}}{\left( {{{{M_1}} \over {{M_2}}}} \right)^{ + 1}}{\left( {{{{T_1}} \over {{T_2}}}} \right)^{ - 2}}$$

WHERE suffix I indicates si system and suffix 2 indicates c.g.s – system

In S.I. system L,M and T are expressed in m, kg,scgs system, L,M and T are expressed in m,g,s

$$x = {\left( {{m \over m}} \right)^1}{\left( {{{kg} \over g}} \right)^1}{\left( {{s \over s}} \right)^{ - 2}}$$

$$ = \left( {{{10}^2}} \right)\left( {{{10}^3}} \right){\left( 1 \right)^{ - 2}}$$

$$x = {10^5}$$

$$ 1 N  = {10^5}dyne$$

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