A student placed two identical spheres A and B as shown in the figure. Then if another ball C identical to A and B is placed in between the balls A and B, determine the ratio of force of attraction between A and B in the two cases.

Explanation

` (##PER_IIT_PHY_VII_C08_E02_060_S01.png" width="80%">
Force of attraction between ball A and B
` F_1 = ( mm)/((2r)^(2)) G,`
Where .m. is the mass of the ball and .r. is the radius of the ball
` F_1 = G (m^(2))/(4 r^(2))`
` (##PER_IIT_PHY_VII_C08_E02_060_S02.png" width="80%">
Force of attraction between A and B after placing the ball C in between them
` F_2 = (Gmm)/((4r)^(2)) = (Gm^(2))/(16 r^(2))`
Ratio of the forces in two cases
` (F_1)/(F_2) = (Gm^(2))/(4r^(2))//(Gm^(2))/(16r^(2)) = (16)/(4) =(4)/(1) = 4 : 1`