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

Explanation

The force of attraction at 2 kg on the 1kg particle
`F_(2) = (GMm)/( d^2) = (G xx 1 xx 2)/( 1^2)`
`F_2 = 2 G`
Similarly `F_3 = (GM m)/( r^2) = (G xx 3 xx 1)/( 1^2)`
`F_3 = 3 G`

Resultant force `F = sqrt(F_2^2 + F_3^2 + 2F_2 F_3 cos theta)`
`= sqrt(4G^(2) + 9G^(2) + 2 xx 2G xx 3G xx cos 60^(@))`
`=sqrt( 4G^(2) + 9G^(2) + 6G^(2))`
`F = sqrt(19) G`