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Motion In Straight Line

Question
CBSEENPH11017641

Two masses m1 and m2 are separated by a distance R. At what distance from m1 the gravitational field will be zero?

Solution
Let the gravitational field be zero at P, which is at a distance x from m1.

Gravitational field at P is zero if the fields due to m1 and m2 are equal and opposite. 

             
i.e.           space Gm subscript 1 over straight x squared equals fraction numerator Gm subscript 2 over denominator left parenthesis straight R minus straight x right parenthesis squared end fraction 
rightwards double arrow        open parentheses fraction numerator straight R minus straight x over denominator straight x end fraction close parentheses squared equals straight m subscript 2 over straight m subscript 1 
rightwards double arrow            fraction numerator straight R minus straight x over denominator straight x end fraction equals square root of straight m subscript 2 over straight m subscript 1 end root 
                     straight R over straight x equals fraction numerator square root of straight m subscript 2 end root plus square root of straight m subscript 1 end root over denominator square root of straight m subscript 1 end root end fraction 
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