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Motion In Straight Line

Question
CBSEENPH11017799

A sphere of mass 40 kg is attracted by a second sphere of mass 60 kg with a force equal to 4 mgf. If G = 6 x 10-11 N m2 kg-2, calculate the distance between them. Acceleration due to gravity = 10 m/s2

Solution

We have, 
Mass, m1 = 40 kg ; m2 = 60 kg
Also, F = 4 mgf = 4 x 10-6 x 10
           = 4 x 10-5 N
G = 6 x 10-11 N mkg-2
Distance between the masses, r = ?

Gravitational force is given by, F = fraction numerator straight G space straight m subscript 1 space straight m subscript 2 over denominator straight r squared end fraction
This implies, 

r = straight r space equals space square root of fraction numerator straight G space straight m subscript 1 space straight m subscript 2 over denominator straight F end fraction end root

space space equals space square root of fraction numerator 6 space straight x space 10 to the power of negative 11 end exponent space straight x space 40 space straight x space 60 over denominator 4 space straight x space 10 to the power of negative 5 end exponent end fraction end root space

space space equals space 0.06 space straight m space equals space 6 space cm