- #1
tanaygupta2000
- 208
- 14
- Homework Statement
- Two particles of masses m1 and m2, interact through a central force potential V(r). At t=0, their position and velocity vectors are given by r1=(0,0,a), r2=(a,0,0), v1=(b,2b,0) and v2=(0,0,3b), where a and b are constants. If m2=2m1, which of the following vectors is perpendicular to the plane of motion?
(a) (2,5,0)
(b) (2,-1,-1)
(c) (-1,2,1)
(d) (1,-3,2)
(e) (1,1,1)
- Relevant Equations
- Position of center of mass, R = (m1r1+m2r2)/(m1+m2)
Velocity of center of mass, V = (m1v1+m2v2)/(m1+m2)
I know that I need to find the equation of the line of motion of the two particles, the dot product of which with one of the options will give 0.
I began with founding the coordinates of center of mass:
R = (m1r1+m2r2)/(m1+m2) = (2a/3, 0, a/3)
and velocity of the center of mass:
V = (m1v1+m2v2)/(m1+m2) = (b/3, 2b/3, 2b)
the mass of the center of mass is given by, m* = m1m2/(m1+m2) = 2m1/3
Now applying law of conservation of momentum, m*V = m1v1 + m2v2
I am getting simply (2b/9, 4b/9, 4b/3) = (b, 2b, 6b)
which doesn't seem to be useful.
Kindly help me in solving this. Thanks !
I began with founding the coordinates of center of mass:
R = (m1r1+m2r2)/(m1+m2) = (2a/3, 0, a/3)
and velocity of the center of mass:
V = (m1v1+m2v2)/(m1+m2) = (b/3, 2b/3, 2b)
the mass of the center of mass is given by, m* = m1m2/(m1+m2) = 2m1/3
Now applying law of conservation of momentum, m*V = m1v1 + m2v2
I am getting simply (2b/9, 4b/9, 4b/3) = (b, 2b, 6b)
which doesn't seem to be useful.
Kindly help me in solving this. Thanks !