Consider three charges `q_(1),q_(2), q_(3)` each equal to q at the vertices of an equilateral triangle of side l. What is the force on a charge Q (with the same sign as q) placed at the centroid of the triangle, as shown in figure ?

Explanation

The resultant force on particle at A due to other two particles is `[becauseF_(AB)=F_(AC)=(Gm^(2))/(a^(2))]`
`F_(A)=sqrt(F_(AB)^(2)+F_(AC)^(2)+2F_(AB)F_(AC)cos60^(@))=sqrt(3)(Gm^(2))/(a^(2))` …(i)
Radius of the circle `r=(2)/(3)xxasin60^(@)=(a)/(sqrt(3))` ....(ii)
From (i) and (ii). `sqrt(3)(mv^(2))/(a)=(Gm^(2)sqrt(3))/(a^(2))impliesv=sqrt((Gm)/(a))`
time period `T=(2pir)/(v)=(2pia)/(sqrt(3))sqrt((a)/(Gm))=2pisqrt((a^(3))/(3Gm))`