Question

Consider a system of three particle having mass 2gm, 4gm and 6gm respectively. CM of the system is
at(1, 1, 1). If a fourth particle having mass 4 gm is added in the system then CM lie at origin. Find the
position of fourth particle.​

Answer 1

Given that,

m

1

=100g

m

2

=150g

m

3

=200g

a = 0.5 m = 50 cm

Now, according to diagram

Center of mass coordinates

X

cm

=

450

0×100+150×50+200×25

X

cm

=

450

7500+5000

X

cm

=27.8cm

X

cm

=0.28m

Now,

Y

cm

=

450

0×100+0×150+

3

×25×200

Y

cm

=

450

8660.3

Y

cm

=19.2cm

Y

cm

=0.2m

Hence, the center of mass of three particles at the vertices of an equilateral triangle is X

cm

=0.28cm and Y

cm

=0.2cm respectively