Multiple choice ? on center of mass

[srhly]

Two balls of masses m1 and m2 are moving along x-axis w/ velocities, v1>v2>0. After transforming from the lab frame to the center-of-mass frame, what are the velocities of m1, v1com, and mass m2, v2com? Vcom is the center of mass velocity for the system of both balls. The choices are:

1.v1com=+v1-Vcom, v2com=+v2+Vcom
2.v1com=+v1-Vcom, v2com=+v2-Vcom
3.v1com=+v1+Vcom, v2com=+v2+Vcom
4.v1com=+Vcom, v2com=+Vcom
5.v1com=+Vcom-v1, v2com=+Vcom+v2
6.v1com=+v1+Vcom, v2com=+v2-Vcom
7.v1com=+Vcom+v1, v2com=+Vcom-v2
7.v1com=+Vcom-v1, v2com=+Vcom-v2
9.v1com=+v2, v2com=+v1

 

[xanthym]

Two balls of masses m1 and m2 are moving along x-axis w/ velocities, v1>v2>0. After transforming from the lab frame to the center-of-mass frame, what are the velocities of m1, v1com, and mass m2, v2com? Vcom is the center of mass velocity for the system of both balls. The choices are:

1.v1com=+v1-Vcom, v2com=+v2+Vcom
2.v1com=+v1-Vcom, v2com=+v2-Vcom
3.v1com=+v1+Vcom, v2com=+v2+Vcom
4.v1com=+Vcom, v2com=+Vcom
5.v1com=+Vcom-v1, v2com=+Vcom+v2
6.v1com=+v1+Vcom, v2com=+v2-Vcom
7.v1com=+Vcom+v1, v2com=+Vcom-v2
7.v1com=+Vcom-v1, v2com=+Vcom-v2
9.v1com=+v2, v2com=+v1

Choice #2
(When transforming to COM Frame, the new apparent entity velocities will be relative to Vcom, that is, Vcom will appear subtracted from v1 & v2.)


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[thepatientmental]

The correct answer is 6. v1com=+v1+Vcom, v2com=+v2-Vcom. This is because in the center-of-mass frame, the total momentum of the system is zero. This means that the velocities in the center-of-mass frame must be equal and opposite for the two balls, with the more massive ball moving slower and the less massive ball moving faster. Therefore, v1com=+v1+Vcom and v2com=+v2-Vcom.