Consistency of units
*Objectives:-
The objective of this challange is to convert given SI unit value of the given quantities tp g,mm & ms unit and also prepare consistant unit system for different unit system.
Value of the following measurements are given as follows:
1)MASS =1kg
2)LENGTH= 1m
3)TIME =1s
4)FORCE =1N
5)STRESS =1Pa
6)ENERGY =1Nm
7)DENSITY =1Kg/m3
8)YOUNG'S Modulus= 210GPa
9)Velocity= 56.33KMPH
10)GRAVITY =9.8m/s2
*conversation of SI unit to g,mm,ms:-
1)Mass:-
-The SI unit of the mass is Kg and value given in the quection is 1 Kg.
-Now we convert in to grams.
we know that, 1kg= 1000 g
conversion factor=1000
2)Length:-
-The SI unit of the length is m and value given in the quection is 1 m.
-Now we convert in to mm.
we know that, 1m= 1000 mm
conversion factor=1000
3)Time:-
-The SI unit of the time is sec and value given in the quection is 1 sec.
-Now we convert in to ms.
we know that, 1m= 1000 ms
conversion factor=1000
4)Force:-
-The SI unit of the force is N and value given in the quection is 1N.
but we know that :- 1N=1Kg*m/S^2 (Derive unit to convert fundamental unit)
Now we convert in to g, mm, ms.
=1000*1000/(1000)^2 g*mm/ms^2
= 1 g*mm/ms^2
5) stress:-
-The SI unit of the stress is N/m^2 and value given in the quection is 1N/m^2.
but we know that :- 1N=1Kg*m/S^2
Then, 1N/m^2=1 kg/m*s^2
Now we convert in to g, mm, ms.
1 kg/m*s^2 = 1000/(1000*(1000)^2) g/mm*ms^2
= 10^-6 g/mm*ms^2
6)Energy:-
-The SI unit of the energy is J and value given in the quection is 1J.
- but, 1J=1N*m
but we know that :- 1N=1Kg*m/S^2
1J= 1Kg*m^2/s^2
Now we convert in to g, mm, ms.
1Kg*m^2/s^2= 1000*(1000)^2/(1000)^2 g*mm^2/ms^2
= 1000 g*mm^2/ms^2
7) Density:-
-The SI unit of the density is Kg/m^3 and value given in the quection is 1Kg/m^3.
Now we convert in to g, mm, ms.
1Kg/m^3= 1000/(1000)^3 g/mm^3
=10^-6 g/mm^3
8) Young's modulus:-
-The SI unit of the Young's modulus is Gpa and value given in the quection is 210 Gpa.
-But, 1Gpa= 10^9 pa= 10^9 N/m^2
Then, 210 gpa= 210*10^9 N/m^2
but we know that :- 1N=1Kg*m/S^2
Then, 1N/m^2=1 kg/m*s^2
Now we convert in to g, mm, ms.
1 kg/m*s^2 = 1000/(1000*(1000)^2) g/mm*ms^2
= 10^-6 g/mm*ms^2
For 210 Gpa:-
210*10^9*10^-6 g/mm*ms^2
210*10^3 g/mm*ms^2
9) Velocity:-
-The SI unit of the velocity is m/s and value given in the quection is 56.33 Kmph.
We know thw equation, 1Kmph= (5/18) m/s
56.33 Kmph= 56.33*5/18= 15.647 m/s
Now we convert in to g, mm, ms.
15.647 m/s= 15.647*1000/1000 mm/ms= 15.647 mm/ms
10) Gravity:-
-The SI unit of the gravity is m/s^2 and value given in the quection is 9.8 m/s^2.
Now we convert in to g, mm, ms.
9.8 m/s^2= 9.8*1000/(1000)^2 mm/ms^2
=9.8*10^-3 mm/ms^2
| no | Quantity | SI unit | convert in to g,mm,ms | Conversion factor |
| 1 | Mass | 1 Kg | 1000 g | 1000 |
| 2 | Length | 1 m | 1000 mm | 1000 |
| 3 | Time | 1 s | 1000 ms | 1000 |
| 4 | Force | 1N | 1 g*mm/ms^2 | 1 |
| 5 | Stress | 1 N/m^2 | 10^-6 g/mm*ms^2 | 10^-6 |
| 6 | Energy | 1 J | 1000 g*mm^2/ms^2 | 1000 |
| 7 | Density | 1Kg/m^3 | 10^-6 g/mm^3 | 10^-6 |
| 8 | Young's modulus | 210 Gpa | 210*10^3 g/mm*ms^2 | 10^3 |
| 9 | velocity | 56.33 Kmph |
15.647 mm/ms |
1 |
| 10 | Gravity | 9.8 m/s^2 | 9.8*10^-3 mm/ms^2 | 10^-3 |
*Table of various unit sytem vs various properties:-
| Unit system | Mass | Length | Time | Force | Stress | Energy | Density | Young's modulus | velocity | Gravity |
| SI unit | 1 Kg | 1 m | 1 s | 1 N | 1 pa | 1 J | 1 Kg/m^3 | 210 Gpa | 15.647 m/s | 9.8 m/s^2 |
| Kg cm ms | 1 Kg | 10^2 cm | 10^3 ms | 10^-4 Kg*cm/ms^2 | 10^-8 Kg/(cm*ms^2) | 10^-2 (Kg*cm^2)/ms^2 | 10^-6 Kg/cm^3 | 2100 Kg/(cm*ms^2) | 1.5647 cm/ms | 9.8e-4 cm/ms^2 |
| Kg cm s | 1 Kg | 10^2 cm | 1 s | 10^2 Kg*cm/s^2 | 10^-2 Kg/(cm*s^2) | 10^4 (Kg*cm^2)/s^2 | 10^-6 Kg/cm^3 | 210e+7 Kg/(cm*s^2) | 1564.7 cm/s | 9.8e+2 cm/s^2 |
| g mm ms | 10^3 g | 10^3 cm | 10^3 ms | 1 g*mm/ms^2 | 10^-6 g/(mm*ms^2) | 10^3 (g*mm^2)/ms^2 | 10^-6 g/mm^3 | 210e+3 g/(mm*ms^2) | 15.647 mm/ms | 9.8e-3 mm/ms^2 |
| g cm s | 10^3 g | 10^2 cm | 1 s | 10^5 g*cm/s^2 | 10 g/(cm*s^2) | 10^7 (g*cm^2)/s^2 | 10^-3 g/cm^3 | 210e+10 g/(cm*s^2) | 1564.7 cm/s | 9.8e+2 cm/s^2 |
| g cm us | 10^3 g | 10^2 cm | 10^6 us | 10^-7 g*cm/us^2 | 10^-11 g/(cm*us^2) | 10^-5 (g*cm^2)/us^2 | 10^-3 g/cm^3 | 2.10 g/(cm*us^2) | 15.647e-4 cm/us | 9.8e-10 cm/us^2 |
| g mm s | 10^3 g | 10^3 cm | 1 s | 10^6 g*mm/s^2 | 1 g/(mm*s^2) | 10^9 (g*mm^2)/s^2 | 10^-6 g/mm^3 | 210e+9 g/(mm*s^2) | 15647 mm/s | 9.8e+3 mm/s^2 |
| ton mm s | 10^-3 g | 10^3 cm | 1 s | 1 ton*mm/s^2 | 10^-6 ton/(mm*s^2) | 10^3 (ton*mm^2)/s^2 | 10^-12 ton/mm^3 | 210e+3 ton/(mm*s^2) | 15647 mm/s | 9.8e+3 mm/s^2 |
| slug ft s | 0.068 slug | 3.28 ft | 1 s | 0.2246 slug*ft/s^2 | 0.0208 slug/(ft*s^2) | 0.7366 (slug*ft^2)/s^2 | 1.93*10^-3 slug/ft^3 | 4.368e+9 slug/(ft*s^2) | 51.322 ft/s | 32.144 ft/s^2 |
| kg mm s | 1 Kg | 10^3 cm | 1 s | 10^3 Kg*mm/s^2 | 10^-3 Kg/(mm*s^2) | 10^6 (Kg*mm^2)/s^2 | 10^-9 Kg/mm^3 | 210e+6 Kg/(mm*s^2) | 15647 mm/s | 9.8e+3 mm/s^2 |
| g cm ms | 10^3 g | 10^2 cm | 10^3 ms | 10^-1 g*cm/ms^2 | 10^-5 g/(cm*ms^2) | 10 (g*cm^2)/ms^2 | 10^-3 g/cm^3 | 210e+4 g/(cm*ms^2) | 1.5647 cm/ms | 9.8e-4 cm/ms^2 |
| kg mm ms | 1 Kg | 10^3 cm | 10^3 ms | 10^-3 Kg*mm/ms^2 | 10^-9 Kg/(mm*ms^2) | 1 (Kg*mm^2)/ms^2 | 10^-9 Kg/mm^3 | 210 Kg/(mm*ms^2) | 15.647 mm/ms | 9.8e-3 mm/ms^2 |
*The conversion factor for parameters in other unit system are as follow:-
1)Kg m s:-
i) Force:- 1 Kg*m/s^2
conversion factor=1
ii) stress:- 1 kg/(m*s^2)
conversion factor=1
iii) Energy:- 1(Kg*m^2)/s^2
conversion factor=1
iv) Density:- 1 Kg/m^3
conversion factor=1
v) Young's modulus:- 210e+9 kg/(m*s^2)
conversion factor=10^9
vi) Velocity:- 15.647 m/s
conversion factor=1
vii) Gravity:- 9.8 m/s^2
conversion factor=1
2) Kg cm ms:-
i) Force:- 10^-4 Kg*cm/ms^2
conversion factor=10^-4
ii) stress:- 10^-8 Kg/(cm*ms^2)
conversion factor=10^-8
iii) Energy:- 10^-2 (Kg*cm^2)/ms^2
conversion factor=10^-2
iv) Density:- 10^-6 Kg/cm^3
conversion factor=10^-6
v) Young's modulus:- 2100 Kg/(cm*ms^2)
conversion factor=10
vi) Velocity:- 1.5647 cm/ms
conversion factor=10^-1
vii) Gravity:- 9.8e-4 cm/ms^2
conversion factor=10^-4
3) Kg cm s:-
i) Force:- 10^2 Kg*cm/s^2
conversion factor=10^2
ii) stress:- 10^-2 Kg/(cm*s^2)
conversion factor=10^-2
iii) Energy:- 10^4 (Kg*cm^2)/s^2
conversion factor=10^4
iv) Density:- 10^-6 Kg/cm^3
conversion factor=10^-6
v) Young's modulus:- 210 Kg/(mm*ms^2)
conversion factor=10^7
vi) Velocity:- 1564.7 cm/s
conversion factor=100
vii) Gravity:- 9.8e+2 cm/s^2
conversion factor=100
4) g mm ms:-
i) Force:- 1 g*mm/ms^2
conversion factor=1
ii) stress:- 10^-6 g/(mm*ms^2)
conversion factor=10^-6
iii) Energy:- 10^3 (g*mm^2)/ms^2
conversion factor=10^3
iv) Density:- 10^-6 g/mm^3
conversion factor=10^-6
v) Young's modulus:- 210e+3 g/(mm*ms^2)
conversion factor=10^3
vi) Velocity:- 15.647 mm/ms
conversion factor=1
vii) Gravity:- 9.8e-3 mm/ms^2
conversion factor=10^-3
5)g cm s:-
i) Force:- 10^5 g*cm/s^2
conversion factor=10^5
ii) stress:- 10 g/(cm*s^2)
conversion factor=10
iii) Energy:- 10^7 (g*cm^2)/s^2
conversion factor=10^+7
iv) Density:- 10^-3 g/cm^3
conversion factor=10^3
v) Young's modulus:- 210e+10 g/(cm*s^2)
conversion factor=10^+10
vi) Velocity:- 1564.7 cm/s
conversion factor=100
vii) Gravity:- 9.8e+2 cm/s^2
conversion factor=100
6) g cm us:-
i) Force:- 10^-7 g*cm/us^2
conversion factor=10^-7
ii) stress:- 10^-11 g/(cm*us^2)
conversion factor=10^-11
iii) Energy:- 10^-5 (g*cm^2)/us^2
conversion factor=10^-5
iv) Density:- 10^-3 g/cm^3
conversion factor=10^-3
v) Young's modulus:- 2.10 g/(cm*us^2)
conversion factor=10^-2
vi) Velocity:- 15.647e-4 cm/us
conversion factor=10^-4
vii) Gravity:- 9.8e-10 cm/us^2
conversion factor=10^-10
7) g mm s:-
i) Force:- 10^6 g*mm/s^2
conversion factor=10^6
ii) stress:- 1 g/(mm*s^2)
conversion factor=1
iii) Energy:- 10^9 (g*mm^2)/s^2
conversion factor=10^9
iv) Density:- 10^-6 g/mm^3
conversion factor=10^-6
v) Young's modulus:- 210e+9 g/(mm*s^2)
conversion factor=10^9
vi) Velocity:- 15647 mm/s
conversion factor=10^3
vii) Gravity:- 9.8e+3 mm/s^2
conversion factor=10^3
8) ton mm s :-
i) Force:- 1 ton*mm/s^2
conversion factor=1
ii) stress:- 10^-6 ton/(mm*s^2)
conversion factor=10^-6
iii) Energy:- 10^3 (ton*mm^2)/s^2
conversion factor=10^3
iv) Density:- 10^-12 ton/mm^3
conversion factor=10^-12
v) Young's modulus:- 210e+3 ton/(mm*s^2)
conversion factor=10^3
vi) Velocity:- 15647 mm/s
conversion factor=10^3
vii) Gravity:- 9.8e+3 mm/s^2
conversion factor=10^3
9) slug ft s:-
i) Force:- 0.2246 slug*ft/s^2
conversion factor=1
ii) stress:- 0.0208 slug/(ft*s^2)
conversion factor=1
iii) Energy:- 0.7366 (slug*ft^2)/s^2
conversion factor=1
iv) Density:- 1.93*10^-3 slug/ft^3
conversion factor=10^-3
v) Young's modulus:- 4.368e+9 slug/(ft*s^2)
conversion factor=10^9
vi) Velocity:- 51.322 ft/s
conversion factor=1
vii) Gravity:- 32.144 ft/s^2
conversion factor=1
10) kg mm s:-
i) Force:- 10^3 Kg*mm/s^2
conversion factor=10^3
ii) stress:- 10^-3 Kg/(mm*s^2)
conversion factor=10^-3
iii) Energy:- 10^6 (Kg*mm^2)/s^2
conversion factor=10^6
iv) Density:- 10^-9 Kg/mm^3
conversion factor=10^-9
v) Young's modulus:- 210e+6 Kg/(mm*s^2)
conversion factor=10^6
vi) Velocity:- 15647 mm/s
conversion factor=10^3
vii) Gravity:- 9.8e+3 mm/s^2
conversion factor=10^3
11) g cm ms:-
i) Force:- 10^-1 g*cm/ms^2
conversion factor=10^-1
ii) stress:- 10^-5 g/(cm*ms^2)
conversion factor=10^-5
iii) Energy:- 10 (g*cm^2)/ms^2
conversion factor=10
iv) Density:- 10^-3 g/cm^3
conversion factor=10^-3
v) Young's modulus:- 210e+4 g/(cm*ms^2)
conversion factor=10^4
vi) Velocity:- 1.5647 cm/ms
conversion factor=10^-1
vii) Gravity:- 9.8e-4 cm/ms^2
conversion factor=10^-4
12) kg mm ms:-
i) Force:- 10^-3 Kg*mm/ms^2
conversion factor=10^-3
ii) stress:- 10^-9 Kg/(mm*ms^2)
conversion factor=10^-9
iii) Energy:- 1 (Kg*mm^2)/ms^2
conversion factor=1
iv) Density:- 10^-9 Kg/mm^3
conversion factor=10^-9
v) Young's modulus:- 210e+9 g/(mm*s^2)
conversion factor=10^9
vi) Velocity:- 15.647 mm/ms
conversion factor=1
vii) Gravity:- 9.8e-3 mm/ms^2
conversion factor=10^-3