Question

Given G in cgs is 6.67 x 10 -8 dyne cm² / g², find its value in mks

Answer 1

soln,

Given,

G=$6.67*10^{-8}dyne cm^2/g^2$

now,

converting:                

1) dyne into Newton,          2) $cm^2$ into $m^2$

   100000dyne=1 N            $(100 cm)^2=1 m^2$

    or, $10^5 dyne= 1 N$           or, 10000 $cm^2$ =$10^4 cm^2= 1 m^2$

   :. 1 dyne = $10^{-5} N$             :. 1$cm^2= 10^{-4} m^2$

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3) $g^2$ into $Kg^2$

$(1000 g)^2 = 1000000 g^2= 10^6 g^2 = 1 kg^2$

:. $1 g^2 = 10^{-6} kg^2$

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Now, through the given, and above derivation replacing dynes into N, cm into m and g into kg for  value of G in MKS system of units,

G =$6.67*10^{-8} dyne cm^2/g^2$

  = $\frac{6.67*10^{-8}* 1 dyne*1cm^2}{1g^2}$

 =   $\frac{6.67*10^{-8}* 10^{-5} N*10^{-4}m^2}{10^-6 kg^2}$

 = $\frac{6.67*10^{(-8-5-4)} Nm^2}{10^{-6} Kg^2}$

 = $6.67*10^{-17} Nm^2*10^6 /kg^2$

 = $6.67*10^{(-17+6)}Nm^2/ kg^2$

 =$6.67*10^{-11} Nm^2/kg^2$