In the question number 25, if the mass placed at vertex A is doubled, then the force acting on the mass 2m placed at the centroid O is

In the question number 25, if the mass placed at vertex A is doubled,

1.	In the question number 25, if the mass placed at vertex A is doubled, then the force acting on the mass 2m placed at the centroid O is
Answer» ZERO `(2Gm^(2))/(l^(2))` `(5Gm^(2))/(l^(2))` `(6Gm^(2))/(l^(2))` Solution :(d) Force on MASS 2m at O due to mass 2m at A is `F'_(OA)=(G(2m)(2m))/((1//sqrt(3))^(2))=(12Gm^(2))/(l^(2))` along OA `:.` The resultant forece on the mass 2m at O due to masses at A,B and C is `F'_(R)=F'_(OA)-(F_(OB) sin30^(@)+F_(OC) sin30^(@))` `(12Gm^(2))/(l^(2))-((6Gm^(2))/(l^(2))xx(1)/(2)+(6Gm^(2))/(l^(2))xx(1)/(2))=0` `= (12Gm^(2))/(l^(2))-(6Gm^(2))/(l^(2))=(6Gm^(2))/(l^(2))` along OA