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  1. Home/
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  3. Week - 1 - Consistency of Units

Week - 1 - Consistency of Units

AIM : To Convert the Given Quantities to different unit systems. The Following are the given quantities  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             These Quantities have…

    • Avinash manjunath

      updated on 16 Feb 2022

    AIM : To Convert the Given Quantities to different unit systems. The Following are the given quantities 

    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

                These Quantities have to be Converted to the following Units

    1. Kg cm ms
    2. Kg cm s
    3. gm mm ms
    4. kg m s
    5. g cm s
    6. g cm us
    7. g mm s
    8. ton mm s
    9. slug ft s
    10. kg mm s
    11. g cm ms
    12. kg mm ms

    ANSWER :

    1.Conversion for the Given SI Unit quantities in the respective desired Unit Systems

      MASS 1Kg Length 1m Time 1s Force 1N Stress 1 Pa Energy 1 Nm Density 1Kg/m3 Young's Modulus 210 Gpa Velocity 56.33 Kmph Gravity 9.8 m/s2
    Kg cm ms 1 kg 100 cm 1000 ms 10-4 kg*cm/(ms)2 1.0197x10-5 Kg/(cm)2 10.197162129779 Kg cm 10-6 kg/(cm)3  210x1013 Kg/(ms)2 *cm 1.564 cm/ms 980x10-6 cm/ms2
    Kg cm s 1 kg 100 cm 1 s 102 Kg*cm/(s)2 1.0197x10-5 Kg/(cm)2 10.197162129779 Kg cm 10-6 kg/(cm)3  210x107 Kg/(s)2 *cm 1564.8 cm/s 980 cm/s2
    Kg m s 1 kg 1 mt 1 s  1 Kg*mt/(s)2 0.1 Kg/(mt)2 0.102 Kg mt 1 Kg/m3  210x109 Kg/(s)2*mt 15.648 m/s 9.8 m/s2
    g cm s 1000 g 100 cm 1s 105 g*cm/s2 1.0197x10-2 g/(cm)2 10197.162129779 g cm  10-3 g/(cm)3  210x1010 g/(s)2 *cm 1564.8 cm/s 980 cm/s2
    g cm us  1000 g 100 cm 106 us 10-7 g*cm/(us)2 1.0197x10-2 g/(cm)2 10197.162129779 g cm  10-3 g/(cm)3 210x10-2 g/(us)2 *cm 1.564x10-3 cm/us 980x10-12 cm/us2
    g mm s 1000 g 1000 mm 1 s 106 g*mm/(s)2 1.0197x10-4 g/(mm)2 101971.62129779 g mm  10-6 g/(mm)3  210x109 g/(s)2 *mm 15648 mm/s 9800 mm/s2
    ton mm s 0.001 ton 1000 mm 1 s 10-3 ton*mm/(s)2 1.0036113565668x10-10 ton/(mm)2  0.10197 ton mm  10-12 ton/(mm)3  210x103 ton/(s)2 *mm 15648 mm/s 9800 mm/s2
    slug ft s 0.0685218 slug 3.28084 ft 1 s 0.224808943 slug*ft/(s)2 0.0208854342 slug/(ft)2   0.2296 slug ft  0.0019403 slug/(ft)3 4.386x109 slug/(s)2 *ft 51.312 ft/s 32.152 ft/s2
    kg mm s  1 kg  1000 mm  1 s  1000 kg*mm/(s)2  1.0197162129779x10-7 Kg/(mm)2  101.97 kg mm  10-9 kg/(mm)3 210x106 kg/s2mm 15648 mm/s 9800 mm/s
    g cm ms  1000 g  100 cm 1000 ms  0.1 g*cm/(ms)2  0.010197162129779 g/(cm)2  10197.162129779 g cm  10-3 g/(cm)3 210x104g/(ms)2cm 1.564 cm/ms 980x10-6 cm/ms2
    kg mm ms  1 kg  1000 mm 1000 ms  10-3 Kg*mm/(ms)2  1.0197162129779x10-7 Kg/(mm)2  101.97 kg mm  10-9 kg/(mm)3 210x102kg/(ms)2mm 15.64 mm/ms 9.8x10-3 mm/s2

    2. Conversion from SI unit to g mm ms unit Systems

            

    • MASS 1kg

                1 kg=1000 g   

    • LENGTH 1m

                  1 mt = 1000 mm

    • TIME 1s

                     1 s =1000 ms

    • FORCE 1N 

                     1N = 1 kg mt/s2s2

                          =   1000 x 1000/(1000)2(1000)2 g mm/(ms)2(ms)2

                          =  1 g mm/s2s2

    • STRESS 1Pa

                            1 pa = 1 Kg/mts2s2

                                    = 1000 / (1000) x (1000)2(1000)2   g/mm(ms)2(ms)2

                                    =  10−610-6   g/mm(ms)2(ms)2

    • ENERGY 1Nm

                          1Nm = 1 kg / s2s2

                                  = 1000/ (1000)2(1000)2 g/s2s2

                                  = 10−310-3 g/s2s2

    • DENSITY 1Kg/m3m3

                            1kg/m3m3= 1000/(1000)3(1000)3 g/mm3mm3

                                              = 10−610-6 g/mm3mm3

    • YOUNG'S Modulus  210GPa

                             210 Gpa = 210 x 109109  Kg/mts2s2

                                            = (210 x 109109x 1000)/(1000)x (1000)2(1000)2 g/mm(ms)2(ms)2

                                            = 210 x 103103 g/mm(ms)2(ms)2

    • Velocity 56.33KMPH

                               56.33 Kmph = (56.33 x 1000)/3600 mt/s

                                                    = 15.64 mt/s

                                                    = (15.64 x 1000)/ (1000) mm/ms 

                                                    = 15.64 mm/ms

    • GRAVITY 9.8m/s2

                                 9.8 m/s2s2 = (9.8 x 1000)/(1000)^2  mm/(ms)2(ms)2

                                                        = 9.8 x 103103 mm/s2s2

     CONCLUSION :   All the given quantities in the SI Unit were converted to the required Unit system successfully.

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