Question

two bodies of masses 3 kg and 12 kg are placed at a distance 12 m. A third body of mass 0.5 kg is to be placed at such a point that the force acting on rhis body is zero. Find the position of that point​

Answer 1

Answer:

To find the place between the two bodies where none of the bodies exert a force on the third body placed in between them

let the force given by 3kg be GM/R²

let the force given by 12kg be = Gm/r²

let the distance of the 3rd object from the 3kg object be => x = R

let the distance of the 3rd object from the 12kg object be => (12-x) = r

Therefore, 3G/x² = 12G/(12-x)²

=> 3(12-x)² = 12x²

=> (12-x)²/x² = 12/3

=> √[12-x/x]² = √4

=> 12-x = 2x

=> 3x = 12

=> 4m

Distance of the 0.5kg object from the 3kg is 4m

and from the 12kg is 8m.

Hope it helped :)