Question

obtain expression for the position vecter of centre of mass of two particle system ​

Answer 1

Explanation:

Center of mass of two masses

(m

1

+m

2

)x

cm

=m

1

x

1

+m

2

x

2

For two masses: x

cm

=

m

1

+m

2

m

1

x

1

+m

2

x

2

Center of mass for N masses

M

tot

r

cm

=∑

i=1

N

m

i

r

i

=m

1

r

1

+m

2

r

2

+m

3

r

3

+⋯+m

N

r

N

r

cm

=

M

tot

1

∑

i=1

N

m

i

r

i

=

M

tot

m

1

r

1

+m

2

r

2

+m

3

r

3

+⋯+m

N

r

N

x

cm

=

M

∑

i=1

N

m

i

x

i

y

cm

=

M

∑

i=1

N

m

i

y

i

z

cm

=

M

∑

i=1

N

m

i

z

i