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

Side of equilateral triangle, a=1m.
Masses at corners= 1 kg, 2kg,3 kg.

Force between 1kg, 2kg=`F_1=G.(2xx1)/(1^2)=2G`
Force between 1kg, 3kg =`F_2=G.(3xx1)/(1^2)=3G`
Now `F_1& F_2` act with an angle of `60^(@)`
Resultant force `F_R=sqrt(F_1^2+F_2^2+2F_1F_2 cos theta)`
`=sqrt(4G^2+9G^2+2xx2xx3G^2xx(1)/(2))`
`=Gsqrt(4+9+6)= sqrt(19)G`.