Question

In system of two particles of masses 'm₁' and 'm₂', the first particle is moved by a distance 'd' towards the centre of mass. To keep the centre of mass unchanged, the second particle will have to be moved by a distance ______.

विकल्प

• `"m"_2/"m"_1 "d"`, towards the centre of mass

• `"m"_1/"m"_2 "d"`, away from the centre of mass

• `"m"_1/"m"_2 "d"`, towards the centre of mass

• `"m"_2/"m"_1 "d"`, away from the centre of mass

Answer 1

In system of two particles of masses 'm₁' and 'm₂', the first particle is moved by a distance 'd' towards the centre of mass. To keep the centre of mass unchanged, the second particle will have to be moved by a distance `underline("m"_1/"m"_2 "d"," towards the centre of mass")`.

Explanation:

Let x₁ and x₂ be the position of masses m, and m₂, respectively.

The position of centre of mass is

`"x"_"CM" = ("x"_1"m"_1 + "x"_2"m"_2)/("m"_1 + "m"_2)`

If Δ x₁ and Δ x₂ be the changes in positions, then change in the position of centre of mass,

`Δ "x"_"CM" = (Δ"x"_1"m"_1 + Δ"x"_2"m"_2)/("m"_1 + "m"_2)`

Given that, the centre of mass remains unchanged i.e., Δ X_CM = 0 and Δ x₁ = d.

`=> 0 = ("dm"_1 + "m"_2 Delta x_2)/("m"_1 + "m"_2)`

or `Delta x_2 = - "m"_1/"m"_2`d

Here, negative sign shows that the second particle should be moved towards the centre of mass.