Plz explain how j sin 30 is written here Three equal masses 2m each are placed at the vertices an equilateral triangle PQR
(i) What is the force acting on a mass m placed at the centroid G Of the tnangle?
(ii) What is the force on mass m if the mass at the vedex P is quadrupled?
Take PG = QG RG = 1 m
2m
2m
. •in: I.-3ö; -
2m
The angle between GR and the positive x-axis is 300. Similarly the angle between
negative x-axis is 300.
G(2m)m
NOW,
(i.e., along positive y-axis)
(—i cos300 - j sin300)
G(2m)m -
(i - j sjn300)
By principle of superposition, we get
GP GO CR
FR = 2Gm2j + 2Gm2(-i cos300-jsin300) + 2Gm2(i cos300- j sin300) - ö
By symmetry all the x-component of the force will cancel out each other.
8Gm2j — 2Gm2 j sin 300 — 2Gm2 sin 300
8Gm2j — 4Gm2 sin 300
= 8Gm2j -2Gm2j
= 6Gm2}
' Yourself
Four point masses each of mass m are kept at the vertices of a square, A point mass
at the point of intersection of the diagonal of a square. What will be the force exper
central mass m?
Hint Use method of symmetry.
Three equal point masses of 1.5 kg each are fixed at the vertices of an equilateral
side 1 m. What is the force acting on a particle of mass 1 kg placed at its centroid
Hint : By superposition principle or by method of symmetry.
