Question

Three equal masses of 1 kg each are placed at the vertices of an equilateral `Delta PQR` and a mass of 2kg is placed at the centroid O of the triangle which is at a distance of `sqrt(2)`m from each the verticles of the triangle. Find the force (in newton) acting on the mass of 2 kg.

Answer 1

Given, `OP =OQ = OR = sqrt(2) m`

The gravitational force on mass 2 kg due to to mass 1 kg at P
`F_(OP)=G(2xx1)/((sqrt(2))^(2))=G` along OP
Similarly, `F_(OQ)=G(2xx1)/((sqrt(2))^(2))=G` along OQ
and `F_(OR)=G(2xx1)/((sqrt(2))^(2))=G` along OR
`F_(OQ) cos 30^(@)` and `F_(OR) cos 30^(@)` are equal and acting in opposite directions, hence cancel out each other
Force on mass 2 kg along OS
`=F_(OQ)sin 30^(@)+F_(OR)sin 30^(@)`
`=2F_(OQ)sin 30^(@)" "(because F_(OQ)=F_(OR))`
`=F_(OQ)`
The resultant force on the mass `2 kg` at `O`,
`F = F_(OP) - F_(OQ)`
`=G-G=0` (zero).