Challenge

Week - 1 - Consistency of units

  Mass Length Time Force Stress Energy Density Youngs modulus velocity gravity
Kg cm ms Kg cm ms 1e+4 N 1e+8 pa  1e+2 J 1e+6 2.1e+3 1.56 9.8e-4
Kg cm s Kg cm s 1e-2 N 1e+2 pa 1e-4 J 1e+6 2.1e+9 1560 981
gm mm ms g mm ms 1 N 1e+6 pa 1e-3 J 1e+6 2.1e+5 15.65 9.8e-3
Kg m s  Kg m s 1 N 1 pa 1 J 1 2.1e+11 15.65 9.81
g cm s g cm s 1e+5 N 1e-1  1e-7 J 1e+3 2.1e+12 1565 981
g cm us g cm us 1e+7 N 1e+11 pa 1e+5 J 1e+3 2.1 1.56e-3 9.81e-10
g mm s g mm s 1e-6 N 1 pa 1e-9 J 1e+6 2.1e+11 1.56e+4 9810
ton mm s  ton  mm s N 1e+6 pa 1e-3 J 1e+12 2.1e+5 1.56e+4 9810
slug ft s slug ft s 4.4 N 47.8 pa 1.36 pa 500 4.32e-9 184.8 32.18
Kg mm s Kg mm s 1e-3 N 1e+3 pa 1e-6 J 1e+9 2.1e+8 15650 9810
g cm ms g cm ms 10 N 1e+5 pa 1e-1 J 1e+3 2.1e+6 1.56 9.81e-4
Kg mm ms Kg mm ms 1e+3 N 1e+9 pa 1 J 1e+9 2.1e+2 15.65 9.81e-3

gm mm ms

stress

`(Kg)/(s^2*m)=(g/(ms^2*mm^2))=((10^3)/((10^3)^2*(10^3)^2))=((10^6)/(10^12))=10^-6`

 Energy

`(Kg*m^2)/s^2=(g*mm^2)/s^2=((10^3*(10^3)^2)/(10^3)^2)=10^9/10^6=10^3`

density

`(Kg)/m^3=(g)/(mm^3)=((10^3)/(10^3)^3)=10^3/10^9=10^-6`

Youngs modulus

`210GPa=210*10^9*(kg)/(s^2*m)=210*10^9*((10^3)/(10^6*10^3))=2.1*10^5`

velocity

`15.65 m/s=15.65((10^3)/10^3)=15.65mm/ms`

gravity

`9.81 m/s^2=9.81 ((10^3)/(10^3)^2)=9.81(10^3/10^6)=9.81*10^-3 (mm)/(ms)`

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