Two particles of masses m and 3m approach each other with different velocities. After collision, the particle of mass m has velocity overset arrow v in their centre of mass frame. Velocity of particle of mass 3m in the centre of mass frame is

Question

Two particles of masses m and 3m approach each other with different velocities. After collision, the particle of mass m has velocity overset arrow v in their centre of mass frame. Velocity of particle of mass 3m in the centre of mass frame is (A) -2 overset arrow v (B) -( overset arrow v/2) (C) -( overset arrow v/3) (D) -( overset arrow v/4)

Tardigrade Admin · Accepted Answer

In the centre of mass frame, the total linear momentum of the system is zero. Hence, m overset arrow v+3m overset arrow v'=0 or overset arrow v'=-( overset arrow v/3)

Q. Two particles of masses $m$ and $3 m$ approach each other with different velocities. After collision, the particle of mass $m$ has velocity $v \to$ in their centre of mass frame. Velocity of particle of mass $3 m$ in the centre of mass frame is

$- 2 v \to$

$- \frac{v \to}{2}$

$- \frac{v \to}{3}$

$- \frac{v \to}{4}$

In the centre of mass frame, the total linear momentum of the system is zero.
Hence, $m v \to + 3 m v \to^{^{'}} = 0$
or $v \to^{^{'}} = - \frac{v \to}{3}$

Q. Two particles of masses m and 3m approach each other with different velocities. After collision, the particle of mass m has velocity v→ in their centre of mass frame. Velocity of particle of mass 3m in the centre of mass frame is

−2v→

−2v→​

−3v→​

−4v→​