particle A makes a elastic collision with another particle B at rest.they fly apart in opposite directions with equal speed.if their masses are Ma and Mb respectively ,then relations between Ma and Mb.
To determine the relationship between the masses Ma and Mb of particles A and B, we can analyze the conservation laws at play during an elastic collision.
In an elastic collision, both momentum and kinetic energy are conserved.
Let's denote the initial velocity of particle A as v₀A, the final velocity of particle A as v₁A, the initial velocity of particle B as 0 (since it is at rest), and the final velocity of particle B as v₁B. Also, let's denote the masses of particles A and B as Ma and Mb, respectively.
Considering momentum conservation, the total initial momentum is equal to the total final momentum.
Initial momentum: Ma * v₀A + Mb * 0 = Ma * v₁A + Mb * v₁B
Since particle B is initially at rest (v₀B = 0), it does not contribute to the initial momentum equation.
Final momentum: Ma * v₁A + Mb * v₁B
Given that the particles fly apart in opposite directions with equal speed, we can assume that the magnitudes of their final velocities are equal:
|v₁A| = |v₁B|
As momentum is a vector quantity, we need to consider the directions as well. Since the particles fly apart in opposite directions, the signs will differ:
v₁A = -v₁B
Substituting the above relation into the momentum conservation equation:
Ma * v₁A + Mb * v₁B = Ma * v₁A - Mb * v₁A
Canceling out the common factor of v₁A, we get:
Mb * v₁A = 0
Since the final velocity v₁A is nonzero (the particles are moving apart), we conclude that:
Mb = 0
This implies that the mass of particle B (Mb) must be zero. Particle B must be massless.
In summary, the relationship between the masses Ma and Mb is that Mb = 0. Particle A has mass (Ma), while particle B is massless (Mb = 0).