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

Explanation

If `F_(1)` is the force of attraction between 1 kg, 2 kg masses, then `F_(1)=F(1xx2)/((1)^(2))impliesF_(1)=2G`

If `F_(2)` is the force of attraction between 1 kg, 3 kg masses, then `F_(2)=Gxx(1xx3)/((1)^(2))impliesF_(2)=3G`
The anglebetween the forces `F_(1)` and `F_(2)` is `60^(@)`. If `F_(R)` is the resultant of these two forces then
`F_(R)=sqrt(F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2)cos theta)`
`impliesF_(r)=sqrt((2G)^(2)+(3G)^(2)+2xx2Gxx3Gxxcos 60^(@))`
`impliesF_(R)=sqrt(19)G`