Three spherical balls of masses 1kg, 2kg and 3kg are placed at the corners of an equilateral triangle of side 1m. Find the magnitude of the gravitational force experted by the 2kg and 3kg masses on the 1kg mass.

Explanation

Mass of the spherical ball at the corner .A. of the equilateral triangle = 1kg
Mass of the spherical ball at the corner .B. of the equilateral triangle = 2kg
Mass of the spherical ball at the comer .C. of the equilateral triangle = 3kg
Side of equilateral triangle = 1m
If .F. is the force of attraction between 1kg, 2kg masses then
`F_1 = G xx (1 xx 2)/((1)^2) rArr F_1 = 2G`
If `.F_2.` is the force of attraction between 1kg, 3kg masses then
` F_2 = G xx (1xx3)/((1)^2) rArr F_2 = 3G`
The angle between the forces `F_1` and `F_2` is `60^@`. If `.F_R.` is the resultant of these two forces, then according to parallelogram law of vectors we can write
`F_R = sqrt(F_1^2 + F_2^2 +2F_1F_2 Cos theta ) rArr F_R = sqrt((2G)^2 + (3G)^2 +2 xx 2G xx 3G xx cos 60^@) rArr F_R = sqrt19 G`