Question

(gravitational)G=6.67x10^-8 cm^3/(g.s^2) by using conversion factors, determine the value of G in SI, English, and Engineering systems of units.

i figure out the SI the answer is (6.67x10^-8 cm^3/g.s^2) * (6.67x10^-14 m^3/6.67x10^-8 cm^3)* (10^3g/1kg)=6.67x10^-11 m^3/kg.s^2. is this correct?

also i dont know how to solve by using english and engineering sysyterms of units.

Answer 1

G=6.67x10^-8 cm^3/(g.s^2)

We know that 1m =100cm =10²cm then 1cm = (1/10²)m

                       1kg =1000grams =10³g then 1g =(1/10³)kg

Now 6.67x10^-8 cm^3/(g.s^2) =6.67x10^-8 (1/10²)^3m³/(1/10³kg.s^2)

                                                =6.67x10^-8 *10^-6*10³m³/(kg.s^2) =6.67x10^-11m³/(kg.s²)

The English Engineering System of Units (commonly called English units)

We know that 1kg = 2.2046lbm

                        1m =3.28084ft

G =  6.67x10^-11m³/(kg.s²) = =6.67x10^-11 *(3.2808)ft³/((2.2046lbm.s²) =106.84*10^-11ft3/lbm.s²

                                                                                                                                                            ⁼ 1.0684*10^-9ft³/lbm.s²