  
r1  r2 r .........(1)

m1 m2
m1  m2


m1 r1  m2 r2
 0 ...(2)
....(3)



m1 r1   m2 r2  m1 r1  m2 (r1  r)


(m1  m2 ) r1  m2 r 
  
m2

r
r .....(4)
 r1 
(m1  m2 )
m1



m1 r1   m2 r2  m2 r2  m1(r2  r)

 r2  

m1
 
r 
r .....(5)
(m1  m2 )
m2
A bost of mass M and length L is floating stationary on the still water in a
lake. A man of mass m, initially standing at one end of the boat, walks to
other end of it and stop; consequently, boat moves on the water. Find
the final displacement of boat (from shore) after it stops considering
there is no resistance offered by water to the boat.
As there is no external force in the direction of displacement, centre of
mass of the system remains constant.

dPSys


d  pi dPCM
 FExt


dt
dt
dt




dPCM
FExt  0 
 0  PCM  MVCM  Const
dt



VCM  Const  VCM  C VCM  0
Centre of mass remain stationary
X CM
L
L
M
(
 x)  m x
M  mL

2
2

M m
M m
L
L
M
(
 x)  m x
M  mL
2
2

M m
M m
mL  (M  m) x  x 
m
L
M m