Question

3. A particle of mass m, is kept at x = 0 and
mass mat 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/m.​

Answer 1

Step-by-step explanation:

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