2 bodies A and b having masses 2kg and 4kg are seperated by 2m. Where should a body of mass 1kg be placed so that the gravitational force on this body due to bodies A and B is zero?

 

Let's say the third body (C) is kept in between the two bodies (A and B) at a distance of 'x' m from B (2-x from A).

 

The gravitational force on C from A and B will be in opposite direction and hence will cancel each other if the magnitude is same.

 

Equating the two forces on body C:

Gives, x = 6.83 or 1.17

 

Since x < 2m (Distance between A and B) (If x is greater than 2 m, it will not be in between A and B and the direction of force by A and B on C will not be opposite nad hence will not cancel each other)

 

Thus x = 1.17.

The third body of mass 1 kg should be kept in between A and B at a distance of 1.17 m from B (or 0.83 m from A).