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There are two bodies of mass 100kg and 10000kg separated by a distance 1m.At what distance from the smaller body is,the intensity of gravitational field will be zero. 

Asked by mritunjaydebnath448 3rd November 2018, 11:23 AM
Answered by Expert

As shown in figure, let a point O be at a distance x m from 100 kg and the intensity of gravitational field at this point
due to the given two masses is zero.
We are interested in intensity of gravitational field at the point O, due to the two given masses 100 kg and 10000 kg.
Hence we need to find the gravitational forces F1 and F2 , which are acting between unit mass placed at O and
each of the two given masses as shwon in figure.
Since we assume intensity at O is zero, then we have F1 = F2...............(1)
hence we have,  begin mathsize 12px style G 100 over x squared space equals space G 10000 over open parentheses 1 minus x close parentheses squared space................ left parenthesis 1 right parenthesis end style
By simplifying eqn.(1), we get begin mathsize 12px style open parentheses fraction numerator x over denominator 1 minus x end fraction close parentheses squared space equals space 1 over 100 space space o r space space space space x space equals space 1 over 11 space m end style
Answered by Expert 4th November 2018, 4:36 AM
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