. Determine the value and units of universal Gravitational constant, G?
 

Solution:
Gravitational force

F=GmMd2

Unit of = Newton(N)
Unit of mass = Kg
Unit of = m
Unit of G = Nm2 Kg-2

We know that acceleration due to gravity near the earth's surface is 9.8 m/s2.
So, gravitational force on an object of mass m near the earth's surface 

​​ mg=GmMd2G=gd2M  
Near the earth's surface we can assume distance between the object and the centre of the earth as,

=Radius of the earth, R=6.4×106 m

The mass of the earth, M=6×1024 kg

So, the value of gravitational constant,

G=gd2M=9.8×6.4×10626×1024=9.8×6.4×6.4×1012-24666×10-126.6×10-11 Nm2kg-2

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