According to the question, the arrangement of the masses is as shown below,
Gravitational force between two masses is given as
F= where,
G= gravitational constant and
r= distance between them.
From the given values, we can say that force between masses at A and G.
= Force between masses at B and G
⇒
FA= and
FB= or
FA=FB==16G ...(i)
[∵ Given,
m1=mA=mB=8‌kg,m2=mG=2‌kg,,
AG=BG=r=1m] From the figure, resultant of
FA and
FB is given as
FAB=√FA2+FB2+2FAFB‌cos‌θ =√2FA2+2FA2‌cos‌120° =√FA2=√(26G)2=16G [from Eq. (i)]
⇒
FAB=FA=FB=16G For resultant force on
2‌kg body to be zero,
4‌kg body should be placed at a certain distance from G such that
FCG=−FAE ⇒
|FCG|=|FAB| or
=G(16) where,
x= distance between
4‌kg and
2‌kg body.
Here,
mC=4‌kg ⇒
=G(16) ⇒
x2= ⇒
x=m This means,
4‌kg body should be placed at point P on line CG such that
PG=m.