- #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 !