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CBSE Class 9 Answered

 A particle of mass m1 is kept at x = 0 and another of mass m2 at x = d. When a third particle is kept at x = d/4, it experiences no net gravitational force due to the two particles. Find m2/m1.
Asked by aahnik.mohanty | 30 Dec, 2017, 10:00: AM
answered-by-expert Expert Answer
gravitatational attractive force between m1 and m is given by
begin mathsize 12px style F subscript 1 space equals space G fraction numerator m cross times m subscript 1 over denominator open parentheses begin display style bevelled d over 4 end style close parentheses squared end fraction space equals space G fraction numerator 16 m cross times m subscript 1 over denominator d squared end fraction end style
gravitational attractive force between m2 and m is given by
begin mathsize 12px style F subscript 2 space equals space G fraction numerator m cross times m subscript 2 over denominator open parentheses begin display style 3 over 4 end style d close parentheses squared end fraction space equals space G fraction numerator 16 m cross times m subscript 2 over denominator 9 d squared end fraction end style
since F1 = F2, we have
 
begin mathsize 12px style G fraction numerator 16 m cross times m subscript 1 over denominator d squared end fraction space equals space G fraction numerator 16 m cross times m subscript 2 over denominator 9 d squared end fraction c a n c e l l i n g space o u t space t h e space c o m m o n space t e r m s comma space w e space g e t space m subscript 2 over m subscript 1 space equals space 9 over 1 end style
 

Answered by | 31 Dec, 2017, 12:33: AM

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