write the expression for velocity of center of mass of two particles of masses m1 and me are moving with velocity v1 and v2
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Answer:
As per center of mass of two objects say 1 and 2 we get then
X=
m
1
+m
2
m
1
x
1
+m
2
x
2
wherex
1
andx
2
are position of obeject 1 and 2 from reference point respectively
Position of object 1 and 2 at time =t
x
1
=v
1
t+x
u
1
x
2
=v
2
t+x
u
2
where x
u
1
andx
u
2
are the initial position of the objects respectively.
Now the center of mass of bjects 1 and 2 at time = t
X(t)=
m
1
+m
2
{m
1
(v
1
t+x
u
1
)+m
2
(v
2
t+x
u
2
)}
Now differentiating with respect to time t, we get
V(t)=
dt
d
{
m
1
+m
2
{m
1
(v
1
t+x
u
1
)+m
2
(v
2
t+x
u
2
)}
}
V=
m
1
+m
2
m
1
v
1
+m
2
v
2
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