Question

Three sperical 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 exerted by `2kg` and `3kg` masses on `1kg` mass.

Answer 1

IF `F_(1)` is the force of attraction between `1kg` and `2kg` masses, then `F_(1)=Gxx(1xx2)/((1)^(2))rArr F_(1)=2G`
if `F_(2)` is the force of attraction between `1kg` and `3kg` masses, then `F_(2)=Gxx(1xx3)/((1)^(2))rArrF_(2)=3G`
The angle between the forces `F_(1)` and `F_(2)` is `60^(@)`. if `F_(R)` is the resultant of these two force `F_(R)=sqrt(F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2)cos theta)`
`rArr F_(R)=sqrt((2G)^(2)+(3G)^(2)+2xx2Gxx3Gxxcos60^(@))`
`rArr F_(R)=sqrt(19)G`