Question

25. Two particles having masses m and 2m are
travelling along x-axis on a smooth surface
with velocities u1, and u2, collide. If their
velocities after collision are v1 and v2, then
the ratio of velocities of their centre of mass
before and after impact is,

1) 2:1

2) 2:3

3) 1:1

4)1:2​

Answer 1

When the two particles having masses m and 2m and travelling along the x-axis with velocities u₁ and u₂ collide then

The ratio of the velocities of centre of mass before and after impact is

1 : 1

Explanation:

The velocity of the centre of mass of the system will change only due to any external force applied on the system.

As there is no external force acting on the system

The velocity of the centre of mass will not change

Therefore,

The velocity of the centre of mass before impact = Velocity of centre of mass after impact

or, Velocity of centre of mass before impact : Velcity of centre of mass after impact = 1 : 1

Hope this answer is helpful.

Know more:

Q: Show that in the absence of any external force, the velocity of the centre of mass remains constant?

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Answer 2

$(3)$ is the correct answer.

Explanation:

Given,

Two particles having masses $m$ and $2m$ are  travelling along x-axis on a smooth surface  with velocities $u_{1}\ and\ u_{2}$ collide. If their  velocities after collision are $v_{1}\ and\ v_{2}$

As there is no external force on two mass system, the velocity of center of mass remains same after collision.

So, The velocity of the center of mass will not change.

The velocity of the center of mass before impact $=$ Velocity of center of mass after impact.

So, The ratio of velocities of their center of mass  before and after impact is $1:1$