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Motion In Straight Line

Question
CBSEENPH11017842

Two bodies of masses 100 kg and 10,000 kg are at a distance 1 m apart. At which point on the line joining them will be the resultant gravitational field intensity zero?

Solution

Let, x be the distance of the point P from 100 kg body where the resultant gravitational intensity is zero. 
Therefore, gravitational intensity at P due to body of mass 100 kg is equal and opposite to that due to body of mass 10, 000 kg. 
Hence, 

space space space space space fraction numerator straight G space straight x space 100 over denominator straight x squared end fraction space equals space fraction numerator straight G space straight x space 10000 over denominator left parenthesis 1 minus straight x right parenthesis squared end fraction

rightwards double arrow space space space 100 space straight x squared space equals space left parenthesis 1 minus straight x right parenthesis squared

rightwards double arrow space space space space space space 10 space straight x space equals space 1 space minus space straight x space

rightwards double arrow space space space space space space 11 space straight x space equals space 1 space

straight i. straight e. comma space straight x space equals space 1 over 11 space straight m
At this point, the gravitational field intensity will be 0.