Week - 1 - Consistency of Units

Aim:

Write the given measurements in the above different system of units. Also, mention the conversion factors.

Kg cm ms

Kg cm s

gm mm ms

kg m s

g cm s

g cm us

g mm s

ton mm s

slug ft s

kg mm s

g cm ms

kg mm ms

Sol :

We have been given the following inputs :

MASS 1kg
LENGTH 1m
TIME 1s
FORCE 1N
STRESS 1Pa
ENERGY 1Nm
DENSITY 1Kg/m3
YOUNG'S Modulus 210GPa
Velocity 56.33KMPH
GRAVITY 9.8m/s2

Now we will express these into different unit systems as shown below :

1.g mm ms

Mass = 1000 kg , Conversion Factor = 10^3

Length = 100 cm , Conversion Factor = 10^3

Time = 1000 ms , Conversion Factor = 10^3

Force = 1 gm mm /ms^2 , Conversion Factor = 10^0

Stress = 10^-6 gm mm /ms^2 , Conversion Factor = 10^-6

Energy = 10^3 gm mm^2 /ms^2 , Conversion Factor = 10^3

Density = 10^-6 g/mm^3 ,Conversion Factor = 10^-6

Youngs Modulus = 210 ^10^3 g /mm ms^2 ,Conversion Factor = 10^-6

Velocity of 56 kmph = 15.64 mm/ms , Conversion Factor = 10^-0

Gravity = 9.8^10^-3 gm mm /ms^2 , Conversion Factor = 10^-3

In the following manner we have created the reference table for different unit systems as shown :