Question

Three equals masses of $mkg$ each are fixed at the vertices of an equilateral triangle $ABC$, a shown in Fig. $8.10$.
(a) What is the force acting on a mass $2m$ placed at the centroid $G$ of the triangle?
(b) What is the force if the mass at the vertex $A$ is doubled?
Take $AG=BG=CG=1m$

Answer 1

R.E.F image

a) As the mass of A,B and C are equal and they are equidistant from G.So,

$F_A=F_B=F_C=F=G\frac{\left(2m\right)\left(m\right)}{(1{)}^2}$

$F=2G{m}^2$

$F_{net}$ on $2m=\overrightarrow{F_A}+\overrightarrow{F_B}+\overrightarrow{F_C}$

$=0N$

b) As $m_A=2m_B=2m_C=2m,$

$F_A=2F_B=2F_C=G\frac{\left(2m\right)\left(2m\right)}{1^2}$

$F=2G{m}^2$

$F_{net}$ on $2matG=\overrightarrow{F_A}+\overrightarrow{F_B}+\overrightarrow{F_C}$

$|F_{net}|=F=2G{m}^2$

$F_{net}=Fj=2GHj$